The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A011781

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A011781

Sextuple factorial numbers: a(n) = Product_{k=0..n-1} (6*k+3).
(history; published version)

#64 by Petros Hadjicostas at Fri Sep 13 22:04:02 EDT 2019

STATUS

editing

proposed

#63 by Petros Hadjicostas at Fri Sep 13 22:03:53 EDT 2019

LINKS

Fatemeh Bagherzadeh, M . Bremner, and S . Madariaga, <a href="http://arxiv.org/abs/1611.01214">Jordan Trialgebras and Post-Jordan Algebras</a>, arXiv:1611.01214 [math.RA], 2016.

Murray Bremner, and Martin Markl, <a href="https://arxiv.org/abs/1809.08191">Distributive laws between the Three Graces</a>, arXiv:1809.08191 [math.AT], 2018.

STATUS

proposed

editing

#62 by Petros Hadjicostas at Fri Sep 13 19:53:29 EDT 2019

STATUS

editing

proposed

#61 by Petros Hadjicostas at Fri Sep 13 19:53:21 EDT 2019

CROSSREFS

Cf. A001147, A035309, A047657, A049308, A069736, A277358, A273464, A277358.

STATUS

proposed

editing

#60 by Petros Hadjicostas at Fri Sep 13 19:50:05 EDT 2019

STATUS

editing

proposed

Discussion

Fri Sep 13

19:51

Petros Hadjicostas: The RHS of Sum(0<=g<=floor(n/2), a(n,g)*y^(n-2*g+1) ) = (2*n-1)!! * Sum(0<=k<=n, 2^k * C(n,k) * C(y,k+1) ) is a G.F., but in Lass' paper y is replaced by N.

#59 by Petros Hadjicostas at Fri Sep 13 19:49:57 EDT 2019

CROSSREFS

Cf. A001147, A035309, A047657, A049308, A069736, A277358, A273464.

#58 by Petros Hadjicostas at Fri Sep 13 19:49:28 EDT 2019

CROSSREFS

Cf. A001147, A047657, A049308, A069736, A277358. , A273464.

STATUS

proposed

editing

#57 by Petros Hadjicostas at Fri Sep 13 19:09:28 EDT 2019

STATUS

editing

proposed

Discussion

Fri Sep 13

19:27

Alois P. Heinz: look here (there is a paper by Lass): https://oeis.org/A035309

19:42

Petros Hadjicostas: A035309 is a triangle, not a rectangular array. OK, I am not an expert in the field, and it is the first time I hear about this formula, but A035309 seems to have a different formula. The Formula section of A035309 does not even seem to have the formula that appears on the RHS of the last equation in the *first* theorem in the paper by Lass (2001). Is it a different Harer-Zagier formula?

19:45

Petros Hadjicostas: OK, A035309 has Sum(0<=g<=floor(n/2), a(n,g)*y^(n-2*g+1) ) = (2*n-1)!! * Sum(0<=k<=n, 2^k * C(n,k) * C(y,k+1) ), but the RHS does not appear in the OEIS... that is probably what I meant...

#56 by Petros Hadjicostas at Fri Sep 13 19:01:50 EDT 2019

LINKS

Fatemeh Bagherzadeh, M Bremner, S Madariaga, <a href="http://arxiv.org/abs/1611.01214">Jordan Trialgebras and Post-Jordan Algebras</a>, arXiv:1611.01214 [math.RA], 2016.

B. Lass, <a href="http://dx.doi.org/10.1016/S0764-4442(01)02049-3">Démonstration combinatoire de la formule de Harer-Zagier</a>, (A combinatorial proof of the Harer-Zagier formula) C. R. Acad. Sci. Paris, Serie I, 333 (3) (2001) No 3, , 155-160.

B. Lass, <a href="http://math.univ-lyon1.fr/~lass/articles/pub3zagier.html">Démonstration combinatoire de la formule de Harer-Zagier</a>, (A combinatorial proof of the Harer-Zagier formula) C. R. Acad. Sci. Paris, Serie I, 333 (3) (2001) No 3, , 155-160.

Valery Liskovets, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL5/Liskovets/liskovets4.html">A Note on the Total Number of Double Eulerian Circuits in Multigraphs </a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.5.

CROSSREFS

Cf. A001147, A047657, A049308, A069736, A277358. A273464.

Cf. A069736, A277358.

STATUS

approved

editing

Discussion

Fri Sep 13

19:09

Petros Hadjicostas: Is there an OEIS rectangular array (read by ascending or descending antidiagonals) that has the Harer-Zagier formula in the first theorem of the paper by Lass (2001)?

#55 by Bruno Berselli at Wed Aug 21 03:19:08 EDT 2019

STATUS

reviewed

approved