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)

#74 by N. J. A. Sloane at Fri Feb 11 04:48:35 EST 2022

STATUS

proposed

approved

#73 by Amiram Eldar at Fri Feb 11 03:43:29 EST 2022

STATUS

editing

proposed

#72 by Amiram Eldar at Fri Feb 11 03:41:37 EST 2022

PROG

(MAGMAMagma) [(3/2)^n*Factorial(2*n)/Factorial(n):n in [0..20]]; // Vincenzo Librandi, May 09 2012

#71 by Amiram Eldar at Fri Feb 11 03:17:12 EST 2022

FORMULA

a(n) = (-3)^n*sum_Sum_{k=0..n} 2^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. [Mircea Merca, May 03 2012]

CROSSREFS

Cf. A001147, A035309, A047657, A048994, A049308, A069736, A273464, A277358.

#70 by Amiram Eldar at Fri Feb 11 03:16:04 EST 2022

LINKS

B. Bodo 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), 155-160.

B. Bodo Lass, <a href="httphttps://math.univ-lyon1doi.fr/~lass/articlesorg/pub3zagier10.html1016/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, Vol. 333(, No. 3) (2001), pp. 155-160; <a href="http://math.univ-lyon1.fr/~lass/articles/pub3zagier.html">alternative link</a>.

#69 by Amiram Eldar at Fri Feb 11 03:13:34 EST 2022

FORMULA

From Amiram Eldar, Feb 11 2022: (Start)

Sum_{n>=0} 1/a(n) = 1 + exp(1/6)*sqrt(Pi/6)*erf(1/sqrt(6)), where erf is the error function.

Sum_{n>=0} (-1)^n/a(n) = 1 - exp(-1/6)*sqrt(Pi/6)*erfi(1/sqrt(6)), where erfi is the imaginary error function. (End)

STATUS

approved

editing

#68 by N. J. A. Sloane at Thu Jan 30 21:29:14 EST 2020

FORMULA

D-finite with recurrence: a(n) +3*(-2*n+1)*a(n-1)=0. - R. J. Mathar, Jan 20 2018

Discussion

Thu Jan 30

21:29

OEIS Server: https://oeis.org/edit/global/2847

#67 by R. J. Mathar at Fri Jan 17 12:59:19 EST 2020

STATUS

editing

approved

#66 by R. J. Mathar at Fri Jan 17 12:59:16 EST 2020

FORMULA

D-finite: a(n) +3*(-2*n+1)*a(n-1)=0. - R. J. Mathar, Jan 20 2018

STATUS

approved

editing

#65 by Alois P. Heinz at Fri Sep 13 22:15:28 EDT 2019

STATUS

proposed

approved