A356588 -id:A356588 - cp's OEIS frontend

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

Seiichi Manyama, Aug 14 2022

nonn

Cf. A354623, A355064, A356554.

Cf. A023887, A356440, A356588.

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

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;

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).

A356590 Expansion of e.g.f. ( Product_{k>0} 1/(1 - (k * x)^k)^(1/k) )^exp(x).

Original entry on oeis.org

1, 1, 8, 96, 2382, 100035, 6995185, 699004551, 96910745876, 17476222963065, 4000562831147323, 1127335505294104887, 384099492016873956422, 155403154609857016567601, 73680868272553092728379865, 40444727351284600806487687057

Offset: 0

Seiichi Manyama, Aug 14 2022

nonn

Cf. A346545, A346547.

Cf. A023881, A356588, A356589.

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

a356589(n) = n!*sum(k=1, n, sigma(k, k)/(k*(n-k)!));
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;

a(0) = 1; a(n) = Sum_{k=1..n} A356589(k) * binomial(n-1,k-1) * a(n-k).

cp's OEIS Frontend

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

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A356590 Expansion of e.g.f. ( Product_{k>0} 1/(1 - (k * x)^k)^(1/k) )^exp(x).

Views

Author

Keywords

Crossrefs

Programs

PARI

PARI

Formula