|
%I #8 Feb 04 2018 16:16:12
%S 1,1,2,6,17,48,132,365,1003,2759,7583,20843,57283,157442,432719,
%T 1189317,3268818,8984318,24693343,67869557,186539251,512702559,
%U 1409161449,3873076007,10645137706,29258128633,80415877302,221022792843,607480469466,1669658209311,4589050472041
%N Expansion of 1/(1 - x*Product_{k>=1} 1/(1 - x^k)^k).
%H Alois P. Heinz, <a href="/A299166/b299166.txt">Table of n, a(n) for n = 0..1000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F G.f.: 1/(1 - x*Product_{k>=1} 1/(1 - x^k)^k).
%F a(0) = 1; a(n) = Sum_{k=1..n} A000219(k-1)*a(n-k).
%p b:= proc(n, k) option remember; `if`(n=0, 1, k*add(
%p b(n-j, k)*numtheory[sigma][2](j), j=1..n)/n)
%p end:
%p a:= n-> add(b(n-j, j), j=0..n):
%p seq(a(n), n=0..35); # _Alois P. Heinz_, Feb 04 2018
%t nmax = 30; CoefficientList[Series[1/(1 - x Product[1/(1 - x^k)^k, {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Antidiagonal sums of A255961.
%Y Cf. A000219, A067687, A299105, A299106, A299108, A299162, A299164, A299167.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Feb 04 2018
|
