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

1, 2, 6, 24, 44, 142, 366, 800, 1636, 4338, 10154, 18968, 42368, 80726, 183914, 401096, 729944, 1402098, 2829814, 5172416, 10600836, 21582558, 37732782, 70148512, 127184636, 236798322, 416265730, 804045376, 1514022088, 2581172630, 4596614522, 8035151408

Offset: 0

Author

Jon Perry, Apr 04 2004

Keywords

• nonn

Comments

Sum of product of i(i+1)-transform of terms in all partitions of n into distinct parts.

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A022629, A265836.

Programs

Mathematica

Take[ CoefficientList[ Expand[ Product[1 + m(m + 1)q^m, {m, 1000}]], q], 30] (* Robert G. Wilson v, Apr 05 2004 *)

Extensions

More terms from Robert G. Wilson v, Apr 05 2004