

A279951


Expansion of Product_{k>=1} 1/(1  x^((k*(k+1)/2)^2)).


0



1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 15, 15, 15, 15, 15, 15, 15, 15, 15, 18, 18, 18, 18, 18, 18, 18, 18, 18, 21, 21, 21, 21, 21, 21, 21, 21, 21, 24, 25, 25, 25, 25, 25, 25
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OFFSET

0,10


COMMENTS

Number of partitions of n into nonzero squared triangular numbers (A000537).


LINKS

Table of n, a(n) for n=0..105.
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226228 (1995), 5772; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226228 (1995), 5772; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
Wikipedia, Squared triangular number
Index entries for related partitioncounting sequences


FORMULA

G.f.: Product_{k>=1} 1/(1  x^((k*(k+1)/2)^2)).


EXAMPLE

a(10) = 2 because we have [9, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].


MATHEMATICA

nmax = 105; CoefficientList[Series[Product[1/(1  x^((k (k + 1)/2)^2)), {k, 1, nmax}], {x, 0, nmax}], x]


CROSSREFS

Cf. A000537, A007294, A068980.
Sequence in context: A111857 A133879 A054898 * A279224 A167383 A167661
Adjacent sequences: A279948 A279949 A279950 * A279952 A279953 A279954


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Dec 23 2016


STATUS

approved



