A356598 - OEIS

%I #11 Aug 15 2022 10:31:03

%S 1,1,8,60,606,6795,96145,1458051,25584020,487911129,10231475323,

%T 230541036627,5647620829862,146760059424017,4075332758190265,

%U 119876230004510557,3727336891407329320,121841674696261466385,4187995620589733257695,150589951713517027739551

%N Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k) )^exp(x).

%F a(0) = 1; a(n) = Sum_{k=1..n} A354340(k) * binomial(n-1,k-1) * a(n-k).

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

%o (PARI) a354340(n) = n!*sum(k=1, n, sumdiv(k, d, d^(k/d+1))/(k*(n-k)!));

%o a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354340(j)*binomial(i-1, j-1)*v[i-j+1])); v;

%Y Cf. A353993, A354340.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 15 2022