A010970 a(n) = binomial(n,17).

1, 18, 171, 1140, 5985, 26334, 100947, 346104, 1081575, 3124550, 8436285, 21474180, 51895935, 119759850, 265182525, 565722720, 1166803110, 2333606220, 4537567650, 8597496600, 15905368710, 28781143380, 51021117810, 88732378800, 151584480450, 254661927156

Offset: 17

Author

N. J. A. Sloane

Keywords

• nonn

Comments

In this sequence there are no primes. - Artur Jasinski, Dec 02 2007

Links

• T. D. Noe, Table of n, a(n) for n = 17..1000
• Milan Janjic, Two Enumerative Functions
• Index entries for linear recurrences with constant coefficients, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[ Binomial(n,17): n in [17..80]]; // Vincenzo Librandi, Mar 26 2011

Maple

seq(binomial(n,17),n=17..37); # Zerinvary Lajos, Aug 06 2008

Mathematica

Table[Binomial[n,17],{n,17,50}] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2011 *)

PARI

for(n=17,50, print1(binomial(n,17), ", ")) \\ G. C. Greubel, Nov 23 2017

Formula

a(n+16) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(n+7)*(n+8)*(n+9)*(n+10)*(n+11)*(n+12)*(n+13)*(n+14)*(n+15)*(n+16)/17!. - Artur Jasinski, Dec 02 2007; R. J. Mathar, Jul 07 2009

G.f.: x^17/(1-x)^18. - Zerinvary Lajos, Aug 06 2008; R. J. Mathar, Jul 07 2009

a(n) = n/(n-17) * a(n-1), n > 17. - Vincenzo Librandi, Mar 26 2011

From Amiram Eldar, Dec 10 2020: (Start)

Sum_{n>=17} 1/a(n) = 17/16.

Sum_{n>=17} (-1)^(n+1)/a(n) = A001787(17)*log(2) - A242091(17)/16! = 1114112*log(2) - 556570716997/720720 = 0.9495520222... (End)