A130410 Alternating row sums of triangle A130191 (Stirling2)^2.

1, -1, -1, 0, 6, 32, 115, 172, -2030, -29013, -250051, -1587556, -5178877, 52922256, 1435509569, 20813187553, 230664704969, 1884809758791, 5120430335582, -216605840330716, -6440821191934686, -122368984222010397, -1842986108839510180, -21473141673616814694

Offset: 0

Author

Wolfdieter Lang Jun 01 2007

Keywords

• sign
• easy

Comments

Stirling2 transform of A000587. 2nd Stirling2 transform of A033999. - Vladimir Reshetnikov, Oct 22 2015

Examples

			E.g.f.: 1 - x - (1/2)*x^2 + (1/4)*x^4+(4/15)*x^5 + (23/144)*x^6 + (43/1260)*x^7 - (29/576)*x^8 - (9671/120960)*x^9 ...
G.f. = 1 - x - x^2 + 6*x^4 + 32*x^5 + 115*x^6 + 172*x^7 - 2030*x^8 - 29013*x^9 + ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..470
• Eric Weisstein's MathWorld, Stirling Transform.
• Eric Weisstein's MathWorld, Bell Polynomial.

Crossrefs

Cf. A048993, A000258 (row sums of A130191), A000587, A033999, A130191.

Programs

Maple

Egf:= 1/exp(exp(exp(x)-1)-1):
S:= series(Egf,x,101):
seq(coeff(S,x,j)*j!, j=0..100); # Robert Israel, Oct 22 2015

Mathematica

Table[Sum[BellY[n, k, -BellB[Range[n]]], {k, 0, n}], {n, 0, 23}] (* Vladimir Reshetnikov, Nov 09 2016 *)

Formula

a(n) = sum(A130191(n,m)*(-1)^m,m=0..n), n>=0.

E.g.f.: 1/exp(f(x)) with f(x):=exp(exp(x)-1)-1.

a(n) = sum(k=0..n, A000587(k)*stirling2(n,k)) = sum(k=0..n, B_k(-1)*stirling2(n,k)), where B_k(x) is k-th Bell polynomial.