A354229 Expansion of e.g.f. 1/(1 - log(1 + x)^3).
1, 0, 0, 6, -36, 210, -630, -5376, 153048, -2194296, 22190760, -93956544, -2677330656, 97821857952, -2019503487456, 27899293618944, -98409183995520, -9548919666829440, 410311098024923520, -10652005874894469120, 176525303194482117120, -46197517147757867520
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-log(1+x)^3))) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=6*sum(j=1, i, binomial(i, j)*stirling(j, 3, 1)*v[i-j+1])); v;
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PARI
a(n) = sum(k=0, n\3, (3*k)!*stirling(n, 3*k, 1));
Formula
a(0) = 1; a(n) = 6 * Sum_{k=1..n} binomial(n,k) * Stirling1(k,3) * a(n-k).
a(n) = Sum_{k=0..floor(n/3)} (3*k)! * Stirling1(n,3*k).