OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
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