A356458 - OEIS

%I #13 Aug 08 2022 09:39:49

%S 1,1,6,38,319,3117,36359,476121,7025708,114118746,2029450055,

%T 39078892305,810834093733,17998186069489,425672049713174,

%U 10676653292086790,283014906314277059,7901659174554937925,231719030698518379003,7118469816302381503209

%N Expansion of e.g.f. ( Product_{k>0} B(x^k) )^(1/(1-x)) where B(x) = exp(exp(x)-1) = e.g.f. of Bell numbers.

%F a(0) = 1; a(n) = Sum_{k=1..n} A355886(k) * binomial(n-1,k-1) * a(n-k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, exp(exp(x^k)-1))^(1/(1-x))))

%o (PARI) a355886(n) = n!*sum(k=1, n, n\k/k!);

%o a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a355886(j)*binomial(i-1, j-1)*v[i-j+1])); v;

%Y Cf. A356025, A356461.

%Y Cf. A000110, A209903, A355886.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 08 2022