A355421 Expansion of e.g.f. exp(Sum_{k=1..3} (exp(k*x) - 1)).
1, 6, 50, 504, 5870, 76872, 1111646, 17522664, 298133054, 5433157512, 105396184478, 2165189912040, 46901678992958, 1067332196912136, 25435754924426270, 633014456504059368, 16411191933603611198, 442258823578968351624
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, 3, exp(k*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, (1+2^j+3^j)*binomial(i-1, j-1)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=1..n} (1 + 2^k + 3^k) * binomial(n-1,k-1) * a(n-k).