A027814 a(n) = 126*(n+1)*binomial(n+5,9)/5.

126, 1512, 9702, 44352, 162162, 504504, 1387386, 3459456, 7963956, 17153136, 34918884, 67721472, 125919612, 225629712, 391270572, 658982016, 1081142370, 1732250520, 2716483770, 4177293120, 6309453150, 9374044680, 13716915030, 19791233280, 28184836680

Offset

4,1

Comments

Number of 15-subsequences of [ 1, n ] with just 5 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 4..1000

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

G.f.: 126*(1+x)*x^4/(1-x)^11.

a(n) = C(n+1, 5)*C(n+5, 5). - Zerinvary Lajos, Apr 18 2005; corrected by R. J. Mathar, Feb 10 2016

From Amiram Eldar, Feb 03 2022: (Start)

Sum_{n>=4} 1/a(n) = 25*Pi^2/6 - 1160419/28224.

Sum_{n>=4} (-1)^n/a(n) = 25*Pi^2/12 - 27625/1344. (End)

Mathematica

Table[126(n+1)Binomial[n+5, 9]/5, {n, 4, 40}]  (* Harvey P. Dale, Mar 13 2011 *)

Crossrefs

Sequence in context: A216588 A297657 A027805 * A109146 A249197 A249212

Adjacent sequences: A027811 A027812 A027813 * A027815 A027816 A027817

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved