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

5,1

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).

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)

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 *)

Crossrefs

Cf. A062190.

Sequence in context: A236350 A364848 A027816 * A194718 A267283 A289349

Adjacent sequences: A027820 A027821 A027822 * A027824 A027825 A027826

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved