cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A299031 #5 Feb 01 2018 20:57:05
%S A299031 1,1,0,3,18,60,252,1576,10494,64152,458400,3407019,27713928,225193982,
%T A299031 1980444648,17626414158,165796077562,1593587604441,15985672426992,
%U A299031 163422639872978,1729188245991060,18743981599820280,208963405365941380,2378065667103672024,27742569814633730608
%N A299031 Number of ordered ways of writing n-th triangular number as a sum of n squares of nonnegative integers.
%H A299031 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%H A299031 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%F A299031 a(n) = [x^(n*(n+1)/2)] (Sum_{k>=0} x^(k^2))^n.
%e A299031 a(3) = 3 because third triangular number is 6 and we have [4, 1, 1], [1, 4, 1] and [1, 1, 4].
%t A299031 Table[SeriesCoefficient[(1 + EllipticTheta[3, 0, x])^n/2^n, {x, 0, n (n + 1)/2}], {n, 0, 24}]
%Y A299031 Cf. A000217, A000290, A066535, A072964, A104383, A126683, A196010, A224677, A224679, A278340, A288126, A298329, A298858, A298938, A299032.
%K A299031 nonn
%O A299031 0,4
%A A299031 _Ilya Gutkovskiy_, Feb 01 2018