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A303907 Expansion of Product_{k>=2} (1 + x^(k*(k+1)/2)). 2
1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 2, 0, 0, 2, 1, 0, 1, 2, 0, 1, 3, 0, 0, 3, 0, 2, 2, 1, 2, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 0, 2, 4, 1, 2, 5, 1, 2, 3, 2, 3, 3, 2, 2, 5, 2, 4, 4, 2, 3, 6, 1, 3, 6, 3, 3, 7, 2, 2, 7, 3, 5, 6, 5, 4, 6, 4, 5, 5, 5, 4, 10, 4, 3, 11, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,22

COMMENTS

Number of partitions of n into distinct triangular numbers > 1.

LINKS

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

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{k=0..n} (-1)^(n-k)*A024940(k).

a(n) ~ exp(3*Pi^(1/3) * ((sqrt(2)-1)*Zeta(3/2))^(2/3) * n^(1/3) / 2^(4/3)) * ((sqrt(2)-1)*Zeta(3/2))^(1/3) / (2^(8/3) * sqrt(3) * Pi^(1/3) * n^(5/6)). - Vaclav Kotesovec, May 04 2018

MATHEMATICA

nmax = 95; CoefficientList[Series[Product[1 + x^(k (k + 1)/2), {k, 2, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000217, A024940, A025147, A280129, A303906.

Sequence in context: A236417 A238304 A219487 * A290870 A244738 A215462

Adjacent sequences:  A303904 A303905 A303906 * A303908 A303909 A303910

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 02 2018

STATUS

approved

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Last modified May 28 14:47 EDT 2020. Contains 334684 sequences. (Running on oeis4.)