A322613 - OEIS

%I #6 Dec 21 2018 03:35:18

%S 1,0,2,9,44,370,3084,32088,336384,4407408,59113440,896773680,

%T 14403234240,250498939392,4625127900288,92232410538240,

%U 1925532322237440,42709138254167040,997150775080043520,24416143271431649280,626110124433676185600,16824255461119247339520,471015493365385119191040

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

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

%p 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

%t nmax = 22; CoefficientList[Series[Product[(1 - Log[1 - x] x^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

%t 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]!

%Y Cf. A126348, A265952, A322612.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Dec 20 2018