A027779 a(n) = 3*(n+1)*binomial(n+2,6).

15, 126, 588, 2016, 5670, 13860, 30492, 61776, 117117, 210210, 360360, 594048, 946764, 1465128, 2209320, 3255840, 4700619, 6662502, 9287124, 12751200, 17267250, 23088780, 30515940, 39901680, 51658425, 66265290, 84275856, 106326528, 133145496, 165562320, 204518160

Offset

4,1

Comments

Number of 9-subsequences of [ 1, n ] with just 2 contiguous pairs.

Links

Table of n, a(n) for n=4..34.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

G.f.: 3*(5+2x)*x^4/(1-x)^8.

a(n) = C(n+1, 5)*C(n+2, 2). - Zerinvary Lajos, May 13 2005; corrected by R. J. Mathar, Feb 10 2016

From Amiram Eldar, Feb 04 2022: (Start)

Sum_{n>=4} 1/a(n) = 5*Pi^2/3 - 2947/180.

Sum_{n>=4} (-1)^n/a(n) = 5*Pi^2/6 + 128*log(2)/3 - 6793/180. (End)

Maple

[seq (stirling2(n+1, n)*binomial(n, 5), n=5..29)]; # Zerinvary Lajos, Dec 06 2006

Mathematica

Table[3 * (n+1) * Binomial[n+2, 6], {n, 4, 50}] (* Amiram Eldar, Feb 04 2022 *)

Crossrefs

Sequence in context: A071080 A193365 A069975 * A337958 A337957 A337956

Adjacent sequences: A027776 A027777 A027778 * A027780 A027781 A027782

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved