A354612 Expansion of e.g.f. exp(f(x) - 1) where f(x) = (1 + x)^x = e.g.f. for A007113.
1, 0, 2, -3, 32, -150, 1404, -11340, 120448, -1319976, 16600320, -223664760, 3300331704, -52223268240, 887583503520, -16071609481200, 309263446333440, -6296705309543040, 135262191966465600, -3056359409652695040, 72462969268541596800
Offset: 0
Keywords
Programs
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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, stirling(j-k, k, 1)/(j-k)!)*binomial(i-1, j-1)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=1..n} A007113(k) * binomial(n-1,k-1) * a(n-k).