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A298329
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Number of ordered ways of writing n^2 as a sum of n squares of nonnegative integers.
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13
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1, 1, 2, 6, 5, 90, 582, 4081, 45678, 378049, 3844532, 39039539, 395170118, 4589810849, 53154371025, 660113986997, 8584476248237, 113555197832758, 1572878837435750, 22259911738401660, 324143769099772448, 4869443438412466557, 74837370448784241452, 1182177603062005007658
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = [x^(n^2)] (Sum_{k>=0} x^(k^2))^n.
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EXAMPLE
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a(3) = 6 because we have [9, 0, 0], [4, 4, 1], [4, 1, 4], [1, 4, 4], [0, 9, 0] and [0, 0, 9].
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MAPLE
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b:= proc(n, i, t) option remember; `if`(n=0, 1/t!, (s->
`if`(s*t<n, 0, add(b(n-s*j, i-1, t-j)/j!, j=0..min(t, n/s))))(i^2))
end:
a:= n-> n!*b(n^2, n$2):
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MATHEMATICA
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Table[SeriesCoefficient[(1 + EllipticTheta[3, 0, x])^n/2^n, {x, 0, n^2}], {n, 0, 23}]
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PROG
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(PARI) {a(n) = polcoeff((sum(k=0, n, x^(k^2)+x*O(x^(n^2))))^n, n^2)} \\ Seiichi Manyama, Oct 28 2018
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CROSSREFS
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[x^(n^b)] (Sum_{k>=0} x^(k^b))^n: A088218 (b=1), this sequence (b=2), A298671 (b=3).
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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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