A027782 a(n) = 9*(n+1)*binomial(n+2,9)/2.

36, 405, 2475, 10890, 38610, 117117, 315315, 772200, 1750320, 3719430, 7482618, 14360580, 26453700, 47006190, 80901810, 135326664, 220641300, 351511875, 548358525, 839188350, 1261890630, 1867083075, 2721610125, 3912807600, 5553662400, 7789011516, 10802941380

Offset

7,1

Comments

Number of 12-subsequences of [ 1, n ] with just 2 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 7..1000

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

Formula

G.f.: 9*(4+x)*x^7/(1-x)^11.

a(n) = binomial(n+1, 8)*binomial(n+2, 2). - Zerinvary Lajos, Apr 28 2005; corrected by R. J. Mathar, Feb 13 2016

From Amiram Eldar, Feb 01 2022: (Start)

Sum_{n>=7} 1/a(n) = 387341/14700 - 8*Pi^2/3.

Sum_{n>=7} (-1)^(n+1)/a(n) = 4*Pi^2/3 + 23552*log(2)/105 - 7435703/44100. (End)

Mathematica

Table[9*(n + 1)*Binomial[n + 2, 9]/2, {n, 7, 40}] (* Stefan Steinerberger, Apr 09 2006 *)

Prog

(Magma) [9*(n+1)*Binomial(n+2, 9)/2: n in [7..33]]; // Vincenzo Librandi, Aug 26 2015

Crossrefs

Sequence in context: A264361 A055862 A105095 * A179099 A181685 A183353

Adjacent sequences: A027779 A027780 A027781 * A027783 A027784 A027785

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved