A303907 Expansion of Product_{k>=2} (1 + x^(k*(k+1)/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

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 A353501 A353428

Adjacent sequences: A303904 A303905 A303906 * A303908 A303909 A303910

Keyword

nonn

Author

Ilya Gutkovskiy, May 02 2018

Status

approved