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 (5,-10,10,-5,1).
FORMULA
a(n) = (8*n^4 +28*n^3 +34*n^2 +17*n+3)/3. - Ralf Stephan, May 15 2007
From G. C. Greubel, Apr 09 2023: (Start)
a(n) = (2*n+1)*binomial(2*n+3, 3).
a(n) = (2*n+1)*A000447(n+1).
G.f.: (1 + 25*x + 35*x^2 + 3*x^3)/(1-x)^5.
E.g.f.: (1/3)*(3 + 87*x + 174*x^2 + 76*x^3 + 8*x^4)*exp(x). (End)
MATHEMATICA
Table[(2*n+1)*Binomial[2*n+3, 3], {n, 0, 50}] (* G. C. Greubel, Apr 09 2023 *)
PROG
(Magma) [(2*n+1)*Binomial(2*n+3, 3): n in [0..50]]; // G. C. Greubel, Apr 09 2023
(SageMath) [(2*n+1)*binomial(2*n+3, 3) for n in range(51)] # G. C. Greubel, Apr 09 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 20 2004
EXTENSIONS
More terms from Hugo Pfoertner, Nov 26 2004
STATUS
approved