The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A262960 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A262960

a(n) = sum(stirling2(n,k)*(k+2)!*(k+3)!, k=1..n)/144.
(history; published version)

#11 by Alois P. Heinz at Mon Oct 05 17:34:14 EDT 2015

STATUS

proposed

approved

#10 by Vaclav Kotesovec at Mon Oct 05 16:58:24 EDT 2015

STATUS

editing

proposed

#9 by Vaclav Kotesovec at Mon Oct 05 16:56:38 EDT 2015

FORMULA

a(n) ~ exp(1/2) * (n+2)! * (n+3)! / 144. - Vaclav Kotesovec, Oct 05 2015

STATUS

proposed

editing

#8 by Michael De Vlieger at Mon Oct 05 15:29:39 EDT 2015

STATUS

editing

proposed

#7 by Michael De Vlieger at Mon Oct 05 15:29:36 EDT 2015

MATHEMATICA

Table[Sum[StirlingS2[n, k] (k + 2)! (k + 3)!, {k, n}]/144, {n, 16}] (* Michael De Vlieger, Oct 05 2015 *)

STATUS

reviewed

editing

#6 by Joerg Arndt at Mon Oct 05 12:45:59 EDT 2015

STATUS

proposed

reviewed

Discussion

Mon Oct 05

14:00

Karol A. Penson: Peter,  unfortunately I have no comment about your guess.

#5 by Alois P. Heinz at Mon Oct 05 11:39:20 EDT 2015

STATUS

editing

proposed

Discussion

Mon Oct 05

12:35

Peter Bala: It also appears that modulo 100 the sequence is periodic with period 4, and modulo 1000 becomes periodic with period 20, and so on. I'll make a wild guess, entirely unsupported by any evidence, that the sequence of periods [1, 4, 20, 100?, 500?, ...] has a rational generating function.

#4 by Alois P. Heinz at Mon Oct 05 11:39:01 EDT 2015

NAME

a(n) = sum(stirling2(n,k)*(k+2)!*(k+3)!, k=1..n)/144.

FORMULA

Representation as a sum of infinite series of special values of hypergeometric functions of type 2F0, in Maple notation: sum(k^n*(k+2)!*(k+3)!*hypergeom([k+3,k+4],[],-1)/k!, k=1..infinity)/144, n=1,2... .

MAPLE

with(combinat): a(:= n) = -> sum(stirling2(n, k)*(k+2)!*(k+3)!, k=1..n)/144: seq(a(n), n=1..20);

STATUS

proposed

editing

#3 by Karol A. Penson at Mon Oct 05 11:32:16 EDT 2015

STATUS

editing

proposed

#2 by Karol A. Penson at Mon Oct 05 11:28:58 EDT 2015

NAME

allocated for Karol A. Penson

a(n) = sum(stirling2(n,k)*(k+2)!*(k+3)!,k=1..n)/144.

DATA

1, 21, 661, 28941, 1678501, 124467021, 11484880261, 1290503997741, 173495416001701, 27499205820027021, 5075028072491665861, 1078923766195953890541, 261780612944688782844901, 71901410584558939807059021, 22195276604290979611365107461, 7651037112318147566092161607341

OFFSET

1,2

COMMENTS

It appears that for all n the last digit of a(n) is 1.

FORMULA

MAPLE

a(n) = sum(stirling2(n, k)*(k+2)!*(k+3)!, k=1..n)/144

CROSSREFS

Cf. A261833.

KEYWORD

allocated

nonn

AUTHOR

Karol A. Penson and Katarzyna Gorska, Oct 05 2015

STATUS

approved

editing