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A267007 Expansion of Product_{k>=1} (1 + (k-1)*x^k).

%I A267007 #10 Aug 15 2019 23:47:24
%S A267007 1,0,1,2,3,6,8,16,20,42,51,92,132,204,299,476,644,978,1488,2024,3048,
%T A267007 4318,6248,8596,12555,17378,24740,34310,47940,65842,93221,125238,
%U A267007 173848,239348,324724,445882,602140,816424,1101096,1495382,1991892,2684252,3598248
%N A267007 Expansion of Product_{k>=1} (1 + (k-1)*x^k).
%H A267007 Vaclav Kotesovec, <a href="/A267007/b267007.txt">Table of n, a(n) for n = 0..10000</a>
%p A267007 b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
%p A267007      `if`(n=0, 1, b(n, i-1)+(i-1)*b(n-i, min(n-i, i-1))))
%p A267007     end:
%p A267007 a:= n-> b(n$2):
%p A267007 seq(a(n), n=0..42);  # _Alois P. Heinz_, Aug 15 2019
%t A267007 nmax = 50; CoefficientList[Series[Product[1+(k-1)*x^k, {k, 1, nmax}], {x, 0, nmax}], x]
%t A267007 nmax = 50; poly = ConstantArray[0, nmax+1]; poly[[1]] = 1; poly[[2]] = 0; Do[Do[poly[[j+1]] += (k-1)*poly[[j-k+1]], {j, nmax, k, -1}];, {k, 2, nmax}]; poly
%Y A267007 Cf. A022629, A162506, A267004, A267008.
%K A267007 nonn
%O A267007 0,4
%A A267007 _Vaclav Kotesovec_, Jan 08 2016