A354239 Expansion of e.g.f. (2 - exp(x))^(x/2).

1, 0, -1, -3, -9, -35, -195, -1477, -13839, -151335, -1877745, -26022491, -398318481, -6674043961, -121496905803, -2387748622365, -50382638237343, -1136006690370371, -27257495551671753, -693436310776781083, -18643640290958926785, -528196548501606911913

Offset

0,4

Links

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

Formula

a(0) = 1; a(n) = (-1/2) * Sum_{k=1..n} A052862(k) * binomial(n-1,k-1) * a(n-k).

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((2-exp(x))^(x/2)))
(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])/2); v;

Crossrefs

Cf. A052862, A354412.

Sequence in context: A005346 A129094 A059424 * A002575 A125792 A223310

Adjacent sequences: A354236 A354237 A354238 * A354240 A354241 A354242

Keyword

sign

Author

Seiichi Manyama, May 26 2022

Status

approved