A113335 a(n) = 3^5 * binomial(n+4, 5).

243, 1458, 5103, 13608, 30618, 61236, 112266, 192456, 312741, 486486, 729729, 1061424, 1503684, 2082024, 2825604, 3767472, 4944807, 6399162, 8176707, 10328472, 12910590, 15984540, 19617390, 23882040, 28857465, 34628958, 41288373, 48934368, 57672648, 67616208

Offset: 1

Author

Zerinvary Lajos, Aug 06 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A027465.

Sequences of the form 3^m*binomial(n+m-1, m): A008585 (m=1), A027468 (m=2), A134171 (m=3), A102741 (m=4), this sequence (m=5).

Programs

Magma

[3^5*Binomial(n+4,5): n in [1..30]]; // G. C. Greubel, May 17 2021

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 *)

Sage

[3^5*binomial(n+4,5) for n in (1..30)] # G. C. Greubel, May 17 2021

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)