A356587 Expansion of e.g.f. ( Product_{k>0} 1/(1 - (k * x)^k)^(1/k) )^x.

1, 0, 2, 15, 236, 8490, 459234, 40325880, 4777773104, 767688946920, 156746202491880, 40056474754165320, 12448131138826294152, 4634982982962988690320, 2033625840922821008112144, 1039060311676326627685615800, 611331728108400284878223051520

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

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).

Prog

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

Crossrefs

Cf. A354623, A355064, A356554.

Cf. A023887, A356440, A356588.

Sequence in context: A212370 A302358 A192561 * A227098 A180610 A156750

Adjacent sequences: A356584 A356585 A356586 * A356588 A356589 A356590

Keyword

nonn

Author

Seiichi Manyama, Aug 14 2022

Status

approved