A355426 Expansion of e.g.f. 1/(1 - Sum_{k=1..3} (exp(k*x) - 1)/k).
1, 3, 24, 284, 4476, 88178, 2084564, 57493334, 1812223276, 64262620538, 2531993864004, 109738634393534, 5188538157065276, 265761817180172498, 14659691726110341844, 866403731832477234134, 54619096812884242006476, 3658454458052874579886058
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, 3, (exp(k*x)-1)/k)))) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (1+2^(j-1)+3^(j-1))*binomial(i, j)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=1..n} (1 + 2^(k-1) + 3^(k-1)) * binomial(n,k) * a(n-k).