A120054 a(n) = binomial(n+3,4)*4^4.

256, 1280, 3840, 8960, 17920, 32256, 53760, 84480, 126720, 183040, 256256, 349440, 465920, 609280, 783360, 992256, 1240320, 1532160, 1872640, 2266880, 2720256, 3238400, 3827200, 4492800, 5241600, 6080256, 7015680, 8055040, 9205760, 10475520, 11872256, 13404160

Offset: 1

Author

Zerinvary Lajos, Aug 07 2008

Keywords

• nonn
• easy

Comments

Number of n permutations (n>=4) of 5 objects u, v, z, x, y with repetition allowed, containing n-4 u's. Example: if n=4 then n-4 = zero (0) u, a(1)=256, if n=5 then n-4 = one (1) u, a(2)=1280, if n=6 then n-4 = two (2) u, a(3)=3840, etc.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A035008, A008586, A038231.

Programs

Maple

seq(binomial(n+3,4)*4^4, n=1..36);

Mathematica

256*Binomial[Range[30]+3,4] (* or *) LinearRecurrence[{5,-10,10,-5,1},{256,1280,3840,8960,17920},30] (* Harvey P. Dale, Jul 19 2018 *)

Formula

G.f.: 256/(1-x)^5.

a(n) = C(n+3,4)*4^4, n>=1.

From Amiram Eldar, Sep 01 2022: (Start)

Sum_{n>=1} 1/a(n) = 1/192.

Sum_{n>=1} (-1)^(n+1)/a(n) = log(2)/8 - 1/12. (End)