A354390 Expansion of e.g.f. 1/(1 + log(1 + x)^4 / 24).
1, 0, 0, 0, -1, 10, -85, 735, -6699, 64764, -662780, 7139000, -80273116, 931853208, -10990479136, 128253707400, -1402525474414, 12224484229744, -9767136488568, -3662083220408136, 144120068237692294, -4329792070579951500, 118808185600297890950
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1+x)^4/24))) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, binomial(i, j)*stirling(j, 4, 1)*v[i-j+1])); v;
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PARI
a(n) = sum(k=0, n\4, (4*k)!*stirling(n, 4*k, 1)/(-24)^k);
Formula
a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n,k) * Stirling1(k,4) * a(n-k).
a(n) = Sum_{k=0..floor(n/4)} (4*k)! * Stirling1(n,4*k)/(-24)^k.