A027780 a(n) = 7*(n+1)*binomial(n+2,7)/2.

21, 196, 1008, 3780, 11550, 30492, 72072, 156156, 315315, 600600, 1089088, 1893528, 3174444, 5155080, 8139600, 12534984, 18877089, 27861372, 40378800, 57557500, 80810730, 111891780, 152956440, 206633700, 276105375, 365195376, 478469376, 621345648, 800217880

Offset

5,1

Comments

Number of 10-subsequences of [ 1, n ] with just 2 contiguous pairs.

Links

Table of n, a(n) for n=5..33.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

G.f.: 7*(3+x)*x^5/(1-x)^9.

a(n) = C(n+1, 6)*C(n+2, 2). - Zerinvary Lajos, Apr 28 2005; corrected by R. J. Mathar, Feb 10 2016

From Amiram Eldar, Feb 04 2022: (Start)

Sum_{n>=5} 1/a(n) = 2969/150 - 2*Pi^2.

Sum_{n>=5} (-1)^(n+1)/a(n) = Pi^2 + 384*log(2)/5 - 3153/50. (End)

Mathematica

Table[7(n+1) Binomial[n+2, 7]/2, {n, 5, 30}] (* Harvey P. Dale, Feb 25 2013 *)

Prog

(PARI) a(n)=7*(n+1)*binomial(n+2, 7)/2 \\ Charles R Greathouse IV, Feb 26 2013

Crossrefs

Sequence in context: A022713 A163718 A164606 * A108679 A200825 A058086

Adjacent sequences: A027777 A027778 A027779 * A027781 A027782 A027783

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Extensions

Offset corrected by Harvey P. Dale, Feb 26 2013

Status

approved