A027817 a(n) = 99*(n+1)*binomial(n+5,12).

792, 11583, 90090, 495495, 2162160, 7963956, 25729704, 74826180, 199536480, 494684190, 1152323172, 2543258718, 5354228880, 10811423700, 21034470600, 39583049220, 72282089880, 128442439125, 222633561150, 377215163325, 625897752480, 1018680525720, 1628611498800

Offset

7,1

Comments

Number of 18-subsequences of [ 1, n ] with just 5 contiguous pairs.

Links

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

Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Formula

G.f.: 99*(8+5x)*x^7/(1-x)^14.

a(n) = C(n+1, 8)*C(n+5, 5). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Feb 10 2016

From Amiram Eldar, Feb 03 2022: (Start)

Sum_{n>=7} 1/a(n) = 1263990883/19209960 - 20*Pi^2/3.

Sum_{n>=7} (-1)^(n+1)/a(n) = 10*Pi^2/3 + 69632*log(2)/693 - 1969871597/19209960. (End)

Mathematica

Table[99(n+1)Binomial[n+5, 12], {n, 7, 30}] (* Harvey P. Dale, Dec 05 2012 *)

Crossrefs

Sequence in context: A282547 A104398 A186057 * A104680 A037190 A209893

Adjacent sequences: A027814 A027815 A027816 * A027818 A027819 A027820

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved