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%I #11 Aug 16 2019 12:52:50
%S 1,2,10,32,120,342,1206,3320,10604,29578,88342,239400,702020,1863654,
%T 5262650,13948824,38427192,100244162,272822282,703972024,1883948848,
%U 4839944150,12779850278,32548367784,85335644100,215826029018,560407835934,1412632075328
%N Expansion of Product_{k>=1} 1/(1 - k*(k+1)*x^k).
%H Vaclav Kotesovec, <a href="/A265836/b265836.txt">Table of n, a(n) for n = 0..2000</a>
%F a(n) ~ c * 6^(n/2), where
%F c = 79.0418032646837469192452349...... if n is even,
%F c = 78.4480460169710091436913691...... if n is odd.
%p b:= proc(n, i) option remember; `if`(n=0 or i=1,
%p 2^n, b(n, i-1)+(1+i)*i*b(n-i, min(n-i, i)))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..33); # _Alois P. Heinz_, Aug 16 2019
%t nmax = 40; CoefficientList[Series[Product[1/(1 - k*(k+1)*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A074141, A077335, A092485, A305204.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Dec 16 2015
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