A354421 Expansion of e.g.f. (2 - exp(x))^x.

1, 0, -2, -6, -12, -10, 60, 406, 672, -18666, -400740, -6617842, -108686952, -1883464466, -34930602252, -693981413610, -14732243810016, -333084114060442, -7994768036250132, -203102355108133154, -5445884954606704920, -153726156157794541986

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1; a(n) = -Sum_{k=1..n} A052862(k) * binomial(n-1,k-1) * a(n-k).

a(n) ~ -n! / (Gamma(1 - log(2)) * 2^(-log(2)) * n^(log(2) + 1) * log(2)^(n - log(2) - 1)). - Vaclav Kotesovec, Jun 08 2022

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((2-exp(x))^x))
(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=1, j-1, (k-1)!*stirling(j-1, k, 2))*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A052862, A354239, A354413.

Sequence in context: A145103 A329654 A009230 * A069491 A127698 A130503

Adjacent sequences: A354418 A354419 A354420 * A354422 A354423 A354424

Keyword

sign

Author

Seiichi Manyama, May 26 2022

Status

approved