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A299166 Expansion of 1/(1 - x*Product_{k>=1} 1/(1 - x^k)^k).

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