A027805 a(n) = 21*(n+1)*binomial(n+4,9).

126, 1470, 9240, 41580, 150150, 462462, 1261260, 3123120, 7147140, 15315300, 31039008, 59961720, 111105540, 198470580, 343219800, 576609264, 943854450, 1509157650, 2362159800, 3626122500, 5468192730, 8112154050, 11854124100, 17081719200, 24297273000

Offset

5,1

Comments

Number of 14-subsequences of [ 1, n ] with just 4 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 5..1000

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

Formula

G.f.: 42*(3+2x)*x^5/(1-x)^11.

a(n) = C(n+1, 6)*C(n+4, 4). - Zerinvary Lajos, May 25 2005; corrected by R. J. Mathar, Feb 13 2016

From Amiram Eldar, Feb 03 2022: (Start)

Sum_{n>=5} 1/a(n) = 1160923/29400 - 4*Pi^2.

Sum_{n>=5} (-1)^(n+1)/a(n) = 2*Pi^2 + 1536*log(2)/35 - 491481/9800. (End)

Mathematica

Table[21(n+1)Binomial[n+4, 9], {n, 5, 30}] (* Harvey P. Dale, Sep 19 2011 *)

Prog

(PARI) a(n)=21*(n+1)*binomial(n+4, 9) \\ Charles R Greathouse IV, Sep 19 2011

Crossrefs

Sequence in context: A002953 A216588 A297657 * A027814 A109146 A249197

Adjacent sequences: A027802 A027803 A027804 * A027806 A027807 A027808

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved