A027765 a(n) = (n+1)*binomial(n+1,5).

5, 36, 147, 448, 1134, 2520, 5082, 9504, 16731, 28028, 45045, 69888, 105196, 154224, 220932, 310080, 427329, 579348, 773927, 1020096, 1328250, 1710280, 2179710, 2751840, 3443895, 4275180, 5267241, 6444032, 7832088, 9460704, 11362120, 13571712, 16128189

Offset: 4

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn
• easy

Comments

Number of 7-subsequences of [ 1, n ] with just 1 contiguous pair.

8*a(n) is the number of permutations of (n+1) symbols that 5-commute with an (n+1)-cycle (see A233440 for definition), where 8 = A000757(5). - Luis Manuel Rivera Martínez, Feb 07 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 4..1000
• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A000757, A233440.

Programs

Magma

[(n+1)*Binomial(n+1,5): n in [4..40]]; // Vincenzo Librandi, Aug 09 2017

Maple

a:=n->(sum((numbcomp(n,6)), j=2..n)):seq(a(n), n=6..34); # Zerinvary Lajos, Aug 26 2008

Mathematica

Table[(n+1)Binomial[n+1,5],{n,4,40}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{5,36,147,448,1134,2520,5082},40] (* Harvey P. Dale, Jan 15 2017 *)

Formula

G.f.: (5+x)*x^4/(1-x)^7.

From Amiram Eldar, Jan 30 2022: (Start)

Sum_{n>=4} 1/a(n) = 5*Pi^2/6 - 575/72.

Sum_{n>=4} (-1)^n/a(n) = 5*Pi^2/12 + 160*log(2)/3 - 2945/72. (End)

Extensions

Incorrect formula deleted by R. J. Mathar, Feb 13 2016