A354610 Expansion of e.g.f. exp(f(x) - 1) where f(x) = (1 - x)^x = e.g.f. for A007114.

1, 0, -2, -3, 16, 90, -84, -2940, -8672, 95256, 956160, -811800, -75724296, -419150160, 4406562720, 78306555600, 89704074240, -9655388184960, -97621097227200, 657339885653760, 23680733504400000, 119677890314505600, -3528587069869276800, -64401874868363598720

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A007114(k) * binomial(n-1,k-1) * a(n-k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((1-x)^x-1)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j!*sum(k=0, j\2, (-1)^(j-k)*stirling(j-k, k, 1)/(j-k)!)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A007114, A354611.

Sequence in context: A012572 A371613 A254382 * A375684 A067848 A269067

Adjacent sequences: A354607 A354608 A354609 * A354611 A354612 A354613

Keyword

sign

Author

Seiichi Manyama, Jul 08 2022

Status

approved