A161254 Number of partitions of n into central polygonal numbers A000124.

1, 1, 2, 2, 4, 4, 6, 7, 10, 11, 14, 17, 21, 24, 29, 34, 41, 46, 55, 62, 73, 81, 96, 107, 124, 137, 158, 175, 199, 221, 250, 276, 310, 343, 383, 421, 469, 516, 572, 626, 693, 757, 833, 908, 1000, 1088, 1192, 1294, 1417, 1535, 1674, 1813, 1974, 2133, 2315, 2501, 2710, 2921

Offset: 0

Author

R. H. Hardin, Jun 06 2009

Keywords

• nonn

Examples

			1 + x + 2*x^2 + 2*x^3 + 4*x^4 + 4*x^5 + 6*x^6 + 7*x^7 + 10*x^8 + 11*x^9 + ...
a(4) = 4 since 4 = 2 + 2 = 2 + 1 + 1 = 1 + 1 + 1 + 1 is a partition in 4 ways. a(7) = 7 since 7 = 4 + 2 + 1 = 4 + 1 + 1 + 1 = 2 + 2 + 2 + 1 = 2 + 2 + 1 + 1 + 1 = 2 + 1 + 1 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1 + 1 is a partition in 7 ways. - _Michael Somos_, May 29 2012
		

Links

• R. H. Hardin, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000124.

Formula

G.f.: 1 / (Product_{k>0} (1 - x^( (k^2 - k)/2 + 1))). - Michael Somos, May 29 2012