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

17,2

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).

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)

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 *)

Prog

(Magma) [ Binomial(n, 17): n in [17..80]]; // Vincenzo Librandi, Mar 26 2011
(PARI) for(n=17, 50, print1(binomial(n, 17), ", ")) \\ G. C. Greubel, Nov 23 2017

Crossrefs

Cf. A001787, A242091.

Sequence in context: A161878 A139618 A162638 * A126920 A341228 A022583

Adjacent sequences: A010967 A010968 A010969 * A010971 A010972 A010973

Keyword

nonn

Author

N. J. A. Sloane

Status

approved