A010972 a(n) = binomial(n,19).

1, 20, 210, 1540, 8855, 42504, 177100, 657800, 2220075, 6906900, 20030010, 54627300, 141120525, 347373600, 818809200, 1855967520, 4059928950, 8597496600, 17672631900, 35345263800, 68923264410, 131282408400, 244662670200, 446775310800, 800472431850

Offset: 19

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 = 19..1000
• Index entries for linear recurrences with constant coefficients, signature (20,-190,1140,-4845,15504,-38760,77520,-125970,167960,-184756,167960,-125970,77520,-38760,15504,-4845,1140,-190,20,-1).

Crossrefs

Cf. A001787, A242091.

Programs

GAP

List([19..45], n-> Binomial(n,19) ); # G. C. Greubel, Aug 27 2019

Magma

[ Binomial(n,19): n in [19..45]]; // Vincenzo Librandi, Mar 26 2011

Maple

seq(binomial(n,19),n=19..39); # Zerinvary Lajos, Aug 04 2008

Mathematica

Table[Binomial[n,19],{n,19,50}] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2011 *)

PARI

vector(25, n, binomial(n+18,19)) \\ G. C. Greubel, Nov 23 2017

SageMath

[binomial(n,19) for n in (19..45)] # G. C. Greubel, Aug 27 2019

Formula

a(n+18) = 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)*(n+17)*(n+18)/19!. - Artur Jasinski, Dec 02 2007; R. J. Mathar, Jul 07 2009

G.f.: x^19/(1-x)^20. - Zerinvary Lajos, Aug 04 2008; R. J. Mathar, Jul 07 2009

a(n) = n/(n-19) * a(n-1), n > 19. - Vincenzo Librandi, Mar 26 2011

From Amiram Eldar, Dec 11 2020: (Start)

Sum_{n>=19} 1/a(n) = 19/18.

Sum_{n>=19} (-1)^(n+1)/a(n) = A001787(19)*log(2) - A242091(19)/18! = 4980736*log(2) - 10574853703013/3063060 = 0.9542064261... (End)