A356335 Expansion of e.g.f. ( Product_{k>0} 1/(1-x^k) )^(1/(1-x)).

1, 1, 6, 39, 332, 3290, 38994, 517986, 7762880, 128029464, 2311675560, 45188359920, 952047539112, 21452758881528, 515073388373712, 13114579450948920, 352881761400606720, 10000259978380933440, 297654582665846499264, 9280441162956638320704

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A356010(k) * 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-x^k))^(1/(1-x))))
(PARI) a356010(n) = n!*sum(k=1, n, sigma(k)/k);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356010(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A000041, A000203, A356010, A356336, A356337.

Sequence in context: A058191 A113347 A265953 * A246571 A031972 A356439

Adjacent sequences: A356332 A356333 A356334 * A356336 A356337 A356338

Keyword

nonn

Author

Seiichi Manyama, Aug 04 2022

Status

approved