A299031 Number of ordered ways of writing n-th triangular number as a sum of n squares of nonnegative integers.

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

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