%I
%S 1,2,6,24,44,142,366,800,1636,4338,10154,18968,42368,80726,183914,
%T 401096,729944,1402098,2829814,5172416,10600836,21582558,37732782,
%U 70148512,127184636,236798322,416265730,804045376,1514022088,2581172630
%N Expansion of Product_{m=>1} (1+m*(m+1)*q^m).
%C Sum of product of i(i+1)transform of terms in all partitions of n into distinct parts.
%H Alois P. Heinz, <a href="/A092485/b092485.txt">Table of n, a(n) for n = 0..1000</a>
%e The partitions of 6 into distinct parts are 6, 1+5, 2+4, 1+2+3, the corresponding i(i+1)transforms are of products 6*7, 2*5*6, 2*3*4*5, 2*2*3*3*4, so 42, 60, 120, 144 and their sum is a(6) = 366.
%t Take[ CoefficientList[ Expand[ Product[1 + m(m + 1)q^m, {m, 1000}]], q], 30]  _Robert G. Wilson v_, Apr 05 2004
%Y Cf. A022629, A265836.
%K nonn
%O 0,2
%A _Jon Perry_, Apr 04 2004
%E More terms from _Robert G. Wilson v_, Apr 05 2004
