OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = 3^5 * binomial(n+4, 5), n >= 1.
From G. C. Greubel, May 17 2021: (Start)
G.f.: 243*x/(1-x)^6.
E.g.f.: (81/40)*x*(120 + 240*x + 120*x^2 + 20*x^3 + x^4)*exp(x). (End)
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=1} 1/a(n) = 5/972.
Sum_{n>=1} (-1)^(n+1)/a(n) = 80*log(2)/243 - 655/2916. (End)
MAPLE
seq(binomial(n+4, 5)*3^5, n=1..27);
MATHEMATICA
With[{c=3^5}, Table[c Binomial[n+4, 5], {n, 30}]] (* Harvey P. Dale, Apr 11 2011 *)
PROG
(Magma) [3^5*Binomial(n+4, 5): n in [1..30]]; // G. C. Greubel, May 17 2021
(Sage) [3^5*binomial(n+4, 5) for n in (1..30)] # G. C. Greubel, May 17 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Aug 06 2008
STATUS
approved