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A338464
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Number of ways to write 2*n as an ordered sum of n squares of positive integers.
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3
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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
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OFFSET
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0,4
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COMMENTS
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Also number of ways to write n as an ordered sum of n nonnegative numbers one less than a square.
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LINKS
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FORMULA
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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.
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MAPLE
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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):
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MATHEMATICA
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Table[SeriesCoefficient[((EllipticTheta[3, 0, x] - 1)/2)^n, {x, 0, 2 n}], {n, 0, 37}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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