A356590 - OEIS

%I #13 Aug 14 2022 15:29:24

%S 1,1,8,96,2382,100035,6995185,699004551,96910745876,17476222963065,

%T 4000562831147323,1127335505294104887,384099492016873956422,

%U 155403154609857016567601,73680868272553092728379865,40444727351284600806487687057

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

%F a(0) = 1; a(n) = Sum_{k=1..n} A356589(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))^exp(x)))

%o (PARI) a356589(n) = n!*sum(k=1, n, sigma(k, k)/(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, a356589(j)*binomial(i-1, j-1)*v[i-j+1])); v;

%Y Cf. A346545, A346547.

%Y Cf. A023881, A356588, A356589.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 14 2022