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A338465
Number of ways to write 2*n as an ordered sum of n nonzero triangular numbers.
2
1, 0, 2, 0, 6, 5, 20, 42, 70, 261, 297, 1430, 1584, 7293, 9634, 35945, 60150, 176596, 366401, 886977, 2150421, 4624410, 12205074, 25065216, 67616872, 139894305, 369551925, 793214982, 2011977414, 4517758504, 10992821055, 25669627965, 60531471286, 145112506352
OFFSET
0,3
COMMENTS
Also number of ways to write n as an ordered sum of n nonnegative numbers one less than a triangular number.
LINKS
FORMULA
a(n) = [x^(2*n)] (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^n, where theta_2() is the Jacobi theta function.
a(n) = [x^n] (Sum_{k>=0} x^(k*(k + 3)/2))^n.
MATHEMATICA
Table[SeriesCoefficient[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^n, {x, 0, 2 n}], {n, 0, 33}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 31 2021
STATUS
approved