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A299031 Number of ordered ways of writing n-th triangular number as a sum of n squares of nonnegative integers. 2
1, 1, 0, 3, 18, 60, 252, 1576, 10494, 64152, 458400, 3407019, 27713928, 225193982, 1980444648, 17626414158, 165796077562, 1593587604441, 15985672426992, 163422639872978, 1729188245991060, 18743981599820280, 208963405365941380, 2378065667103672024, 27742569814633730608 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..24.

Index entries for sequences related to sums of squares

Index to sequences related to polygonal numbers

FORMULA

a(n) = [x^(n*(n+1)/2)] (Sum_{k>=0} x^(k^2))^n.

EXAMPLE

a(3) = 3 because third triangular number is 6 and we have [4, 1, 1], [1, 4, 1] and [1, 1, 4].

MATHEMATICA

Table[SeriesCoefficient[(1 + EllipticTheta[3, 0, x])^n/2^n, {x, 0, n (n + 1)/2}], {n, 0, 24}]

CROSSREFS

Cf. A000217, A000290, A066535, A072964, A104383, A126683, A196010, A224677, A224679, A278340, A288126, A298329, A298858, A298938, A299032.

Sequence in context: A012779 A327768 A074439 * A210366 A000648 A235988

Adjacent sequences:  A299028 A299029 A299030 * A299032 A299033 A299034

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 01 2018

STATUS

approved

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Last modified July 29 01:22 EDT 2021. Contains 346340 sequences. (Running on oeis4.)