A356440 - OEIS

%I #8 Aug 07 2022 12:59:25

%S 1,1,8,99,2444,101450,7045194,701736966,97147459184,17505366041880,

%T 4005462950166600,1128394974054308400,384386423684496873672,

%U 155497732356686080354968,73718160600338917089657216,40462026280443230503858113240

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

%F a(0) = 1; a(n) = Sum_{k=1..n} A356437(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)^(1/k))^(1/(1-x))))

%o (PARI) a356437(n) = n!*sum(k=1, n, sigma(k, 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, a356437(j)*binomial(i-1, j-1)*v[i-j+1])); v;

%Y Cf. A356437, A356439.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 07 2022