A082114 - OEIS

%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