A354518 Expansion of e.g.f. cosh(x)^exp(x).
1, 0, 1, 3, 7, 30, 166, 798, 4117, 27660, 196756, 1328448, 9866407, 86205210, 759842266, 6460661028, 60841732777, 651349676280, 6795873687496, 67981177154688, 770224145659627, 9854500496860470, 116983085896035646, 1301594922821009028, 17440543467561038557
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..486
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(cosh(x)^exp(x))) -
PARI
a354520(n) = sum(k=1, n\2, (16^k-4^k)*bernfrac(2*k)/(2*k)*binomial(n, 2*k)); a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354520(j)*binomial(i-1, j-1)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=1..n} A354520(k) * binomial(n-1,k-1) * a(n-k).
Comments