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A303905 Expansion of (1/(1 - x))*Product_{k>=1} (1 + x^(k*(k+1)/2)). 0
1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 9, 10, 10, 11, 12, 13, 15, 16, 17, 19, 20, 22, 24, 24, 26, 29, 30, 31, 34, 36, 37, 41, 44, 44, 47, 50, 52, 56, 59, 62, 65, 67, 70, 73, 75, 79, 85, 89, 91, 96, 100, 102, 108, 113, 116, 123, 129, 132, 137, 142, 147, 153, 158, 162, 169, 176, 182, 190, 196, 201 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A024940.

LINKS

Table of n, a(n) for n=0..69.

Index entries for sequences related to partitions

FORMULA

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

MATHEMATICA

nmax = 69; CoefficientList[Series[1/(1 - x) Product[1 + x^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000217, A024940, A036469, A038348, A061208, A248801, A302835, A303668.

Sequence in context: A082774 A074239 A248333 * A237638 A334483 A261093

Adjacent sequences:  A303902 A303903 A303904 * A303906 A303907 A303908

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 02 2018

STATUS

approved

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Last modified July 2 09:21 EDT 2020. Contains 335398 sequences. (Running on oeis4.)