A298435 - OEIS

A298435

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

1, 2, 3, 6, 9, 12, 20, 28, 36, 52, 70, 88, 120, 156, 192, 250, 318, 386, 488, 606, 727, 900, 1101, 1308, 1590, 1916, 2257, 2706, 3225, 3768, 4465, 5270, 6117, 7178, 8399, 9686, 11274, 13094, 15020, 17352, 20017, 22846, 26230, 30080, 34175, 39010, 44500, 50346, 57184, 64914, 73156

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OFFSET

0,2

COMMENTS

Number of partitions of n into triangular numbers of 2 kinds.

Self-convolution of A007294.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Index entries for related partition-counting sequences

FORMULA

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

a(n) ~ exp(3*(Pi/2)^(1/3) * Zeta(3/2)^(2/3) * n^(1/3)) * Zeta(3/2)^(5/3) / (2^(29/6) * sqrt(3) * Pi^(5/3) * n^(13/6)). - Vaclav Kotesovec, Apr 08 2018

EXAMPLE

a(3) = 6 because we have [3a], [3b], [1a, 1a, 1a], [1a, 1a, 1b], [1a, 1b, 1b] and [1b, 1b, 1b].

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[1/(1 - x^(k (k + 1)/2))^2, {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000217, A000712, A007294, A279225.

Sequence in context: A144677 A309677 A058616 * A261539 A325552 A271882

Adjacent sequences: A298432 A298433 A298434 * A298436 A298437 A298438

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 19 2018

STATUS

approved