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A298329 Number of ordered ways of writing n^2 as a sum of n squares of nonnegative integers. 12
1, 1, 2, 6, 5, 90, 582, 4081, 45678, 378049, 3844532, 39039539, 395170118, 4589810849, 53154371025, 660113986997, 8584476248237, 113555197832758, 1572878837435750, 22259911738401660, 324143769099772448, 4869443438412466557, 74837370448784241452, 1182177603062005007658 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..100 (first 81 terms from Seiichi Manyama)

Index entries for sequences related to sums of squares

FORMULA

a(n) = [x^(n^2)] (Sum_{k>=0} x^(k^2))^n.

EXAMPLE

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].

MAPLE

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):

seq(a(n), n=0..25);  # Alois P. Heinz, Oct 28 2018

MATHEMATICA

Table[SeriesCoefficient[(1 + EllipticTheta[3, 0, x])^n/2^n, {x, 0, n^2}], {n, 0, 23}]

PROG

(PARI) {a(n) = polcoeff((sum(k=0, n, x^(k^2)+x*O(x^(n^2))))^n, n^2)} \\ Seiichi Manyama, Oct 28 2018

CROSSREFS

[x^(n^b)] (Sum_{k>=0} x^(k^b))^n: A088218 (b=1), this sequence (b=2), A298671 (b=3).

Cf. A037444, A066535, A232173, A287617, A298330, A300446.

Sequence in context: A175350 A085057 A069113 * A009462 A111119 A107495

Adjacent sequences:  A298326 A298327 A298328 * A298330 A298331 A298332

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 17 2018

STATUS

approved

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Last modified March 29 21:32 EDT 2020. Contains 333117 sequences. (Running on oeis4.)