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
Keywords
Programs
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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;
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