A356587 - OEIS

%I #10 Aug 14 2022 10:15:54

%S 1,0,2,15,236,8490,459234,40325880,4777773104,767688946920,

%T 156746202491880,40056474754165320,12448131138826294152,

%U 4634982982962988690320,2033625840922821008112144,1039060311676326627685615800,611331728108400284878223051520

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

%F a(0) = 1, a(1) = 0; a(n) = Sum_{k=2..n} k! * sigma_{k-1}(k-1)/(k-1) * 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))^x))

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j!*sigma(j-1, j-1)/(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;

%Y Cf. A354623, A355064, A356554.

%Y Cf. A023887, A356440, A356588.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 14 2022