login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Expansion of Product_{k>=1} 1/(1 - k*x^k/(1 - x)^k).
1

%I #8 Apr 03 2019 09:04:14

%S 1,1,4,13,42,130,397,1197,3566,10517,30760,89293,257397,737220,

%T 2099215,5945594,16756258,47004829,131286914,365203797,1012031772,

%U 2794446326,7690009600,21094325177,57687762889,157306741287,427777384499,1160250104637,3139067594584,8472525405830,22815639395641

%N Expansion of Product_{k>=1} 1/(1 - k*x^k/(1 - x)^k).

%C First differences of the binomial transform of A006906.

%p a:=series(mul(1/(1-k*x^k/(1-x)^k),k=1..100),x=0,31): seq(coeff(a,x,n),n=0..30); # _Paolo P. Lava_, Apr 03 2019

%t nmax = 30; CoefficientList[Series[Product[1/(1 - k x^k/(1 - x)^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A006906, A218482, A307262, A318127, A320563.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Apr 01 2019