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A161254 Number of partitions of n into central polygonal numbers A000124. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

EXAMPLE

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

CROSSREFS

Cf. A000124.

Sequence in context: A029008 A240844 A136343 * A241313 A241317 A185224

Adjacent sequences:  A161251 A161252 A161253 * A161255 A161256 A161257

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jun 06 2009

STATUS

approved

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Last modified November 14 01:24 EST 2019. Contains 329108 sequences. (Running on oeis4.)