A318580 Expansion of e.g.f. exp(-1 + Product_{k>=1} 1/(1 - x^k)^k).

1, 1, 7, 55, 601, 7561, 116191, 1999327, 39267985, 850964401, 20332107991, 527930427751, 14838001344937, 447653776595065, 14440021169407471, 495398956418435791, 18012260306904120481, 691502230924473978337, 27948692251661337581095, 1185878351946613955122711

Offset

0,3

Links

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

Formula

E.g.f.: exp(-1 + exp(Sum_{k>=1} sigma_2(k)*x^k/k)).

E.g.f.: A(x) = exp(B(x) - 1), where B(x) = o.g.f. of A000219.

a(0) = 1; a(n) = Sum_{k=1..n} A000219(k)*k!*binomial(n-1,k-1)*a(n-k).

Maple

seq(n!*coeff(series(exp(-1+mul(1/(1-x^k)^k, k=1..100)), x=0, 20), x, n), n=0..19); # Paolo P. Lava, Jan 09 2019

Mathematica

nmax = 19; CoefficientList[Series[Exp[-1 + Product[1/(1 - x^k)^k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 19; CoefficientList[Series[Exp[-1 + Exp[Sum[DivisorSigma[2, k] x^k/k, {k, 1, nmax}]]], {x, 0, nmax}], x] Range[0, nmax]!
p[n_] := p[n] = Sum[DivisorSigma[2, k] p[n - k], {k, n}]/n; p[0] = 1; a[n_] := a[n] = Sum[p[k] k! Binomial[n - 1, k - 1] a[n - k], {k, n}]; a[0] = 1; Table[a[n], {n, 0, 19}]

Crossrefs

Cf. A000219, A001157, A058892, A318250.

Sequence in context: A083836 A326885 A159313 * A054910 A028562 A209668

Adjacent sequences: A318577 A318578 A318579 * A318581 A318582 A318583

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 29 2018

Status

approved