A027816 a(n) = 66*(n+1)*binomial(n+5,11).

462, 6336, 46332, 240240, 990990, 3459456, 10618608, 29405376, 74826180, 177365760, 395747352, 838053216, 1695505812, 3294910080, 6177956400, 11218384320, 19791524610, 34015101120, 57085528500, 93740446800, 150886065330, 238437239040, 370429282080

Offset

6,1

Comments

Number of 17-subsequences of [ 1, n ] with just 5 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 6..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.: 66*(7+5x)*x^6/(1-x)^13.

a(n) = C(n+1, 7)*C(n+5, 5). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Feb 10 2016

a(n)= 13*a(n-1)- 78*a(n-2)+ 286*a(n-3)-715*a(n-4)+1287*a(n-5)- 1716*a(n-6)+ 1716*a(n-7)- 1287*a(n-8)+ 715*a(n-9)- 286*a(n-10)+ 78*a(n-11)-13*a(n-12)+a (n-13). - Harvey P. Dale, Dec 27 2015

From Amiram Eldar, Feb 03 2022: (Start)

Sum_{n>=6} 1/a(n) = 35*Pi^2/6 - 10445563/181440.

Sum_{n>=6} (-1)^n/a(n) = 35*Pi^2/12 + 512*log(2)/9 - 12377237/181440. (End)

Mathematica

Table[66(n+1)Binomial[n+5, 11], {n, 6, 50}] (* or *) LinearRecurrence[ {13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1}, {462, 6336, 46332, 240240, 990990, 3459456, 10618608, 29405376, 74826180, 177365760, 395747352, 838053216, 1695505812}, 40] (* Harvey P. Dale, Dec 27 2015 *)

Crossrefs

Sequence in context: A154056 A236350 A364848 * A027823 A194718 A267283

Adjacent sequences: A027813 A027814 A027815 * A027817 A027818 A027819

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved