A322613 Expansion of e.g.f. Product_{k>=1} (1 - log(1 - x)*x^k).

1, 0, 2, 9, 44, 370, 3084, 32088, 336384, 4407408, 59113440, 896773680, 14403234240, 250498939392, 4625127900288, 92232410538240, 1925532322237440, 42709138254167040, 997150775080043520, 24416143271431649280, 626110124433676185600, 16824255461119247339520, 471015493365385119191040

Offset: 0

Author

Ilya Gutkovskiy, Dec 20 2018

Keywords

• nonn

Crossrefs

Cf. A126348, A265952, A322612.

Programs

Maple

seq(coeff(series(factorial(n)*mul((1-log(1-x)*x^k),k=1..n),x,n+1), x, n), n = 0 .. 22); # Muniru A Asiru, Dec 21 2018

Mathematica

nmax = 22; CoefficientList[Series[Product[(1 - Log[1 - x] x^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 22; CoefficientList[Series[Exp[Sum[Sum[(-1)^(d + 1) Log[1/(1 - x)]^d/d, {d, Divisors[k]}] x^k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

Formula

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