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
Alois P. Heinz, Table of n, a(n) for n = 0..2000
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