

A299031


Number of ordered ways of writing nth 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
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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



