A027783 a(n) = 5*(n+1)*binomial(n+2,10).

45, 550, 3630, 17160, 65065, 210210, 600600, 1555840, 3719430, 8314020, 17551820, 35271600, 67897830, 125847260, 225544440, 392251200, 663966875, 1096717050, 1771619850, 2804201400, 4356527175, 6652824750, 9999397200, 14809766400, 21636143100, 31208497320

Offset

8,1

Comments

Number of 13-subsequences of [ 1, n ] with just 2 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 8..1000

Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Formula

G.f.: 5*(9+2x)*x^8/(1-x)^12.

a(n) = C(n+1, 9)*C(n+2, 2). - Zerinvary Lajos, May 13 2005; corrected by R. J. Mathar, Mar 15 2016

From Amiram Eldar, Feb 01 2022: (Start)

Sum_{n>=8} 1/a(n) = 3*Pi^2 - 5218691/176400.

Sum_{n>=8} (-1)^n/a(n) = 3*Pi^2/2 + 13312*log(2)/35 - 49112821/176400. (End)

Mathematica

Table[5(n+1)Binomial[n+2, 10], {n, 8, 30}] (* Harvey P. Dale, Jan 21 2012 *)

Crossrefs

Sequence in context: A223047 A147842 A349849 * A160837 A160838 A189350

Adjacent sequences: A027780 A027781 A027782 * A027784 A027785 A027786

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved