|
%I #12 Dec 22 2022 02:24:27
%S 1,2,8,28,79,190,406,792,1437,2458,4004,6260,9451,13846,19762,27568,
%T 37689,50610,66880,87116,112007,142318,178894,222664,274645,335946,
%U 407772,491428,588323,699974,828010,974176,1140337,1328482,1540728
%N Diagonal sums of number array A082105.
%H G. C. Greubel, <a href="/A082107/b082107.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^5 + 20*n^3 + 9*n + 30)/30.
%F G.f.: (1-4*x+11*x^2-10*x^3+6*x^4)/(1-x)^6 . - _R. J. Mathar_, Mar 27 2019
%F E.g.f.: (1/30)*(30 +30*x +75*x^2 +45*x^3 +10*x^4 +x^5)*exp(x). - _G. C. Greubel_, Dec 22 2022
%t LinearRecurrence[{6,-15,20,-15,6,-1}, {1,2,8,28,79,190}, 51] (* _G. C. Greubel_, Dec 22 2022 *)
%o (Magma) [(n^5+20*n^3+9*n+30)/30: n in [0..50]]; // _G. C. Greubel_, Dec 22 2022
%o (SageMath) [(n^5+20*n^3+9*n+30)/30 for n in range(51)] # _G. C. Greubel_, Dec 22 2022
%Y Cf. A082043, A082045, A082046, A082105, A082106, A082109, A082110.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Apr 03 2003
|
