login
A082114
Diagonal sums of number array A082110.
2
1, 2, 9, 32, 89, 210, 441, 848, 1521, 2578, 4169, 6480, 9737, 14210, 20217, 28128, 38369, 51426, 67849, 88256, 113337, 143858, 180665, 224688, 276945, 338546, 410697, 494704, 591977, 704034, 832505, 979136, 1145793, 1334466, 1547273
OFFSET
0,2
FORMULA
a(n) = (n+1)*(n^4 - n^3 + 26*n^2 - 26*n + 30)/30.
From G. C. Greubel, Dec 22 2022: (Start)
G.f.: (1 - 4*x + 12*x^2 - 12*x^3 + 7*x^4)/(1-x)^6.
E.g.f.: (1/30)*(30 + 30*x + 90*x^2 + 50*x^3 + 10*x^4 + x^5)*exp(x). (End)
MATHEMATICA
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 2, 9, 32, 89, 210}, 51] (* G. C. Greubel, Dec 22 2022 *)
PROG
(Magma) [(n+1)*(n^4-n^3+26*n^2-26*n+30)/30: n in [0..50]]; // G. C. Greubel, Dec 22 2022
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 04 2003
STATUS
approved