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A092485 Expansion of Product_{m=>1} (1+m*(m+1)*q^m). 2

%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

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Last modified February 16 21:46 EST 2020. Contains 331975 sequences. (Running on oeis4.)