A027781 a(n) = 4*(n+1)*binomial(n+2,8).

28, 288, 1620, 6600, 21780, 61776, 156156, 360360, 772200, 1555840, 2975544, 5441904, 9573720, 16279200, 26860680, 43147632, 67663332, 103831200, 156227500, 230887800, 335675340, 480720240, 678939300

Offset

6,1

Comments

Number of 11-subsequences of [ 1, n ] with just 2 contiguous pairs.

Links

Table of n, a(n) for n=6..28.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

G.f.: 4*(7+2*x)*x^6/(1-x)^10.

a(n) = C(n+1, 7)*C(n+2, 2). - Zerinvary Lajos, May 13 2005

a(n) = 10*a(n-1)- 45*a(n-2) +120*a(n-3) -210*a(n-4) +252*a(n-5) -210*a(n-6) +120*a(n-7) -45*a(n-8) +10*a(n-9) -a(n-10). - Harvey P. Dale, May 20 2012

From Amiram Eldar, Feb 04 2022: (Start)

Sum_{n>=6} 1/a(n) = 7*Pi^2/3 - 48277/2100.

Sum_{n>=6} (-1)^n/a(n) = 7*Pi^2/6 + 1984*log(2)/15 - 649921/6300. (End)

Mathematica

Drop[Table[4(n+1)Binomial[n+2, 8], {n, 30}], 5] (* or *) LinearRecurrence[ {10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {28, 288, 1620, 6600, 21780, 61776, 156156, 360360, 772200, 1555840}, 30] (* Harvey P. Dale, May 20 2012 *)

Crossrefs

Sequence in context: A107418 A183484 A241621 * A219626 A126662 A156711

Adjacent sequences: A027778 A027779 A027780 * A027782 A027783 A027784

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Extensions

Offset corrected by Harvey P. Dale, May 20 2012

Status

approved