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%I #6 Sep 14 2018 14:28:34
%S 1,2,0,24,144,960,4608,74048,859952,9568800,109975680,1647979872,
%T 23917274304,358378620704,5528847787008,94307761212304,
%U 1632598198916544,29205907283227776,538335591996965760,10388234139989630128,205386383159397554688,4173254005731822569088
%N Number of ordered ways of writing n-th triangular number as a sum of n squares.
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F a(n) = [x^(n*(n+1)/2)] theta_3(x)^n, where theta_3() is the Jacobi theta function.
%F a(n) = [x^(n*(n+1)/2)] (Sum_{k=-infinity..infinity} x^(k^2))^n.
%t Table[SeriesCoefficient[EllipticTheta[3, 0, x]^n, {x, 0, n (n + 1)/2}], {n, 0, 21}]
%t Join[{1}, Table[SquaresR[n, n (n + 1)/2], {n, 21}]]
%Y Cf. A000217, A000290, A066535, A196010, A232173, A278340, A298858, A299031, A299032.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Sep 13 2018
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