A027823 a(n) = 77*(n+1)*binomial(n+6,11).

462, 6468, 48048, 252252, 1051050, 3699696, 11435424, 31855824, 81477396, 193993800, 434546112, 923410488, 1873980108, 3651858672, 6864396000, 12493200720, 22086194130, 38030772780, 63935791920, 105157552500, 169513974630, 268241893920, 417265168320

Offset: 5

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn
• easy

Comments

Number of 18-subsequences of [ 1, n ] with just 6 contiguous pairs.

Links

• T. D. Noe, Table of n, a(n) for n = 5..1000
• Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Crossrefs

Cf. A062190.

Programs

Mathematica

Table[77(n+1) Binomial[n+6,11],{n,5,40}] (* or *) LinearRecurrence[{13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1},{462,6468,48048,252252,1051050,3699696,11435424,31855824,81477396,193993800,434546112,923410488,1873980108},30] (* Harvey P. Dale, Oct 20 2016 *)

Formula

G.f.: 462*(1+x)*x^5/(1-x)^13.

a(n) = C(n+1, 6)*C(n+6, 6). - Zerinvary Lajos, Jun 08 2005; corrected by R. J. Mathar, Feb 13 2016

From Amiram Eldar, Feb 04 2022: (Start)

Sum_{n>=5} 1/a(n) = 10446403/176400 - 6*Pi^2.

Sum_{n>=5} (-1)^(n+1)/a(n) = 3*Pi^2 - 82899/2800. (End)