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%I #14 May 31 2012 22:38:05
%S 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,
%T 137,158,175,199,221,250,276,310,343,383,421,469,516,572,626,693,757,
%U 833,908,1000,1088,1192,1294,1417,1535,1674,1813,1974,2133,2315,2501,2710,2921
%N Number of partitions of n into central polygonal numbers A000124.
%H R. H. Hardin, <a href="/A161254/b161254.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: 1 / (Product_{k>0} (1 - x^( (k^2 - k)/2 + 1))). - _Michael Somos_, May 29 2012
%e 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 + ...
%e 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
%Y Cf. A000124.
%K nonn
%O 0,3
%A _R. H. Hardin_, Jun 06 2009