A023882 Expansion of g.f.: 1/Product_{n>0} (1 - n^n * x^n).

1, 1, 5, 32, 304, 3537, 52010, 895397, 18016416, 410889848, 10523505770, 298220329546, 9274349837081, 313761671751672, 11474635626789410, 450964042480390679, 18954785687060988578, 848386888530723146912

Offset: 0

Author

Olivier Gérard

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..380

Crossrefs

Cf. A265949, A292312, A294645.

Programs

Magma

m:=20; R:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-k^k*x^k): k in [1..m]]) )); // G. C. Greubel, Oct 30 2018

Maple

seq(coeff(series(1/mul(1-k^k*x^k,k=1..n),x,n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 31 2018

Mathematica

nmax=20; CoefficientList[Series[Product[1/(1-k^k*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 19 2015 *)

PARI

m=20; x='x+O('x^m); Vec(prod(k=1, m, 1/(1-k^k*x^k))) \\ G. C. Greubel, Oct 30 2018

Formula

Log of g.f.: Sum_{k>=1} (sigma(k, k+1)/k) x^k, where sigma(k, q) is the sum of the q-th powers of the divisors of k.

a(n) ~ n^n * (1 + exp(-1)/n + (1/2*exp(-1)+5*exp(-2))/n^2). - Vaclav Kotesovec, Dec 19 2015

a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} A294645(k)*a(n-k) for n > 0. - Seiichi Manyama, Nov 09 2017