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%I #11 Dec 23 2022 07:52:20
%S 1,2,9,32,89,210,441,848,1521,2578,4169,6480,9737,14210,20217,28128,
%T 38369,51426,67849,88256,113337,143858,180665,224688,276945,338546,
%U 410697,494704,591977,704034,832505,979136,1145793,1334466,1547273
%N Diagonal sums of number array A082110.
%H G. C. Greubel, <a href="/A082114/b082114.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) = (n+1)*(n^4 - n^3 + 26*n^2 - 26*n + 30)/30.
%F From _G. C. Greubel_, Dec 22 2022: (Start)
%F G.f.: (1 - 4*x + 12*x^2 - 12*x^3 + 7*x^4)/(1-x)^6.
%F E.g.f.: (1/30)*(30 + 30*x + 90*x^2 + 50*x^3 + 10*x^4 + x^5)*exp(x). (End)
%t LinearRecurrence[{6,-15,20,-15,6,-1}, {1,2,9,32,89,210}, 51] (* _G. C. Greubel_, Dec 22 2022 *)
%o (Magma) [(n+1)*(n^4-n^3+26*n^2-26*n+30)/30: n in [0..50]]; // _G. C. Greubel_, Dec 22 2022
%o (SageMath) [(n+1)*(n^4-n^3+26*n^2-26*n+30)/30 for n in range(51)] # _G. C. Greubel_, Dec 22 2022
%Y Cf. A082045, A082107, A082110.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Apr 04 2003
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