The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A355004

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A355004

a(n) = Sum_{k=0..n} A271703(k + n, n), row sums of A355005.
(history; published version)

#10 by Peter Luschny at Wed Jun 15 11:52:46 EDT 2022

STATUS

editing

approved

#9 by Peter Luschny at Wed Jun 15 11:51:17 EDT 2022

FORMULA

a(n) = A187535(n) * hypergeom([1, -n], [1 - 2*n, -2*n], -1].

CROSSREFS

Cf. A271703 (unsigned Lah), A355005, A187535.

STATUS

proposed

editing

#8 by Vaclav Kotesovec at Wed Jun 15 05:55:59 EDT 2022

STATUS

editing

proposed

Discussion

Wed Jun 15

06:21

Peter Luschny: Wow!

#7 by Vaclav Kotesovec at Wed Jun 15 05:55:47 EDT 2022

FORMULA

From Vaclav Kotesovec, Jun 15 2022: (Start)

Recurrence: (n-1)^2 * n * (64*n^4 - 464*n^3 + 1244*n^2 - 1475*n + 663)*a(n) = (n-1)*(2*n-3)*(512*n^6 - 3968*n^5 + 11872*n^4 - 17336*n^3 + 12880*n^2 - 4597*n + 617)*a(n-1) + (2048*n^7 - 19968*n^6 + 78912*n^5 - 163216*n^4 + 191140*n^3 - 128857*n^2 + 48842*n - 8937)*a(n-2) + 4*(2*n-5)*(2*n-3)*(64*n^4 - 208*n^3 + 236*n^2 - 123*n + 32)*a(n-3).

a(n) ~ 2^(4*n - 1/2) * n^(n - 1/2) / (sqrt(Pi) * exp(n)). (End)

#6 by Vaclav Kotesovec at Wed Jun 15 05:44:53 EDT 2022

MATHEMATICA

Table[Sum[Binomial[n + k, n]*FactorialPower[n + k - 1, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jun 15 2022 *)

#5 by Vaclav Kotesovec at Wed Jun 15 05:40:18 EDT 2022

CROSSREFS

Cf. A271703 (unsigned Lah), A355005.

STATUS

proposed

editing

#4 by Peter Luschny at Wed Jun 15 05:38:29 EDT 2022

STATUS

editing

proposed

#3 by Peter Luschny at Wed Jun 15 05:17:29 EDT 2022

NAME

allocated for Peter Luschnya(n) = Sum_{k=0..n} A271703(k + n, n), row sums of A355005.

DATA

1, 3, 43, 1333, 63321, 4034341, 321994723, 30869387193, 3454384526353, 441903886812721, 63608031487665171, 10174227287873082853, 1790258521269694523113, 343669522619597368671933, 71473405251333054552561091, 16008271911444915765782477041, 3841639137772270982094393928353

OFFSET

0,2

MAPLE

L := (n, k) -> ifelse(n = k, 1, binomial(n-1, k-1)*n! / k!):

seq(add(L(n + k, n), k = 0..n), n = 0..16);

CROSSREFS

A271703 (unsigned Lah), A355005.

KEYWORD

allocated

nonn

AUTHOR

Peter Luschny, Jun 15 2022

STATUS

approved

editing

#2 by Peter Luschny at Wed Jun 15 04:53:23 EDT 2022

KEYWORD

allocating

allocated

#1 by Peter Luschny at Wed Jun 15 04:53:23 EDT 2022

NAME

allocated for Peter Luschny

KEYWORD

allocating

STATUS

approved