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A338464 Number of ways to write 2*n as an ordered sum of n squares of positive integers. 3
1, 0, 0, 3, 0, 0, 15, 0, 8, 84, 0, 110, 495, 0, 1092, 3018, 120, 9520, 18870, 2907, 77520, 120270, 43890, 606188, 780023, 531300, 4620200, 5161377, 5651100, 34622172, 35045340, 55234560, 256503672, 245772464, 508930224, 1886151225, 1788167610, 4491607230 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Also number of ways to write n as an ordered sum of n nonnegative numbers one less than a square.
LINKS
FORMULA
a(n) = [x^(2*n)] ((theta_3(x) - 1) / 2)^n, where theta_3() is the Jacobi theta function.
a(n) = [x^n] (Sum_{k>=0} x^(k*(k + 2)))^n.
a(n) = A337165(2n,n). - Alois P. Heinz, Feb 04 2021
MAPLE
b:= proc(n, t) option remember;
`if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
`if`(s>n, 0, b(n-s, t-1)))(j^2), j=1..isqrt(n))))
end:
a:= n-> b(2*n, n):
seq(a(n), n=0..39); # Alois P. Heinz, Feb 04 2021
MATHEMATICA
Table[SeriesCoefficient[((EllipticTheta[3, 0, x] - 1)/2)^n, {x, 0, 2 n}], {n, 0, 37}]
CROSSREFS
Sequence in context: A208848 A277945 A169777 * A278208 A105786 A291802
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 31 2021
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)