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%I #17 Dec 22 2023 10:48:02
%S 12,3480,695776,146278160,24075289500,2757589446360,199926892967040,
%T 9002136703356360,266012140249399740,5540786512741512384,
%U 86568566944442320608,1065719011381263788328,10740917528961226530924
%N Number of n X n arrays of squares of integers summing to 15.
%C There are either one 9, one 4 and two 1's, or one 9 and six 1's, or three 4's and three 1's, or two 4's and seven 1's, or one 4 and eleven 1's, or fifteen 1's, and in each case the rest are 0's. - _Robert Israel_, Jun 04 2020
%H R. H. Hardin, <a href="/A159395/b159395.txt">Table of n, a(n) for n = 2..100</a>
%H <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (31, -465, 4495, -31465, 169911, -736281, 2629575, -7888725, 20160075, -44352165, 84672315, -141120525, 206253075, -265182525, 300540195, -300540195, 265182525, -206253075, 141120525, -84672315, 44352165, -20160075, 7888725, -2629575, 736281, -169911, 31465, -4495, 465, -31, 1).
%F Empirical G.f.: -4*x^2*(1+x)*(3 + 774*x + 147595*x^2 + 31420746*x^3 +4930813594*x^4 + 514132877008*x^5 + 30735972011770*x^6 +965001688149346*x^7 + 16097428576776773*x^8 +150031357184487178*x^9 + 818650552471356653*x^10 +2702659491995569492*x^11 + 5503456361992829612*x^12 +6971617718513038912*x^13 + 5503456361992829612*x^14 +2702659491995569492*x^15 + 818650552471356653*x^16 +150031357184487178*x^17 + 16097428576776773*x^18 +965001688149346*x^19 + 30735972011770*x^20 + 514132877008*x^21 +4930813594*x^22 + 31420746*x^23 + 147595*x^24 + 774*x^25 + 3*x^26)/(-1+x)^31. - _Vaclav Kotesovec_, Nov 30 2012
%F From _Robert Israel_, Jun 04 2020: (Start) Empirical g.f. confirmed.
%F a(n) = (n^30 - 105*n^28 + 5005*n^26 - 110565*n^24 + 587587*n^22 + 25750725*n^20 - 572127985*n^18 + 4357458105*n^16 + 651498848*n^14 - 209929880160*n^12 + 1338174481280*n^10 - 3184977017040*n^8 + 1625807456064*n^6 + 3390523799040*n^4 - 2964061900800*n^2)/15!. (End)
%p seq((n^30 - 105*n^28 + 5005*n^26 - 110565*n^24 + 587587*n^22 + 25750725*n^20 - 572127985*n^18 + 4357458105*n^16 + 651498848*n^14 - 209929880160*n^12 + 1338174481280*n^10 - 3184977017040*n^8 + 1625807456064*n^6 + 3390523799040*n^4 - 2964061900800*n^2)/15!, n=2..30); # _Robert Israel_, Jun 04 2020
%K nonn,easy
%O 2,1
%A _R. H. Hardin_, Apr 11 2009