A121869 Monthly Problem 10791, first expression.

-1, 1, 0, -5, -15, 104, 1827, 7893, -207000, -5646249, -47897675, 1479282600, 74711288407, 1396956334921, -21032523700672, -2719998717430365, -104158663871982343, -715846242343471272, 189941380201812700699, 14820744271258596866013, 507768838531742620183176

Offset: 0

Author

N. J. A. Sloane, Sep 05 2006

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..330
• A. Fekete and G. Martin, Problem 10791: Squared Series Yielding Integers, Amer. Math. Monthly, 108 (No. 2, 2001), 177-178.

Crossrefs

Cf. A121870, A024429, A024430, A121867, A121868.

Programs

GAP

List([0..25], n-> (-1)*Sum([0..n], k-> Stirling2(n,k)) *Sum([0..n], k-> (-1)^k*Stirling2(n,k)) ); # G. C. Greubel, Oct 08 2019

Magma

a:= func< n | (-1)*(&+[StirlingSecond(n,k): k in [0..n]])*(&+[ (-1)^k*StirlingSecond(n,k): k in [0..n]]) >;
[a(n): n in [0..25]]; // G. C. Greubel, Oct 08 2019

Maple

with(combinat): seq(-bell(n)*BellB(n, -1), n = 0..25); # G. C. Greubel, Oct 08 2019

Mathematica

Table[-BellB[n]*BellB[n, -1], {n,0,25}] (* G. C. Greubel, Oct 08 2019 *)

PARI

a(n) = (-1)*sum(k=0,n, stirling(n,k,2))*sum(k=0,n, (-1)^k*stirling(n,k,2));
vector(25, n, a(n-1)) \\ G. C. Greubel, Oct 08 2019

Sage

[ -sum(stirling_number2(n, k) for k in (0..n))*sum((-1)^k* stirling_number2(n,k) for k in (0..n)) for n in (0..25)] # G. C. Greubel, Oct 08 2019

Formula

a(n) = A024429(n)^2 - A024430(n)^2.