A017757 Binomial coefficients C(n,93).

1, 94, 4465, 142880, 3464840, 67910864, 1120529256, 16007560800, 202095455100, 2290415157800, 23591276125340, 223044792457760, 1951641934005400, 15913388077274800, 121623751733457400, 875691012480893280, 5965645022526085470, 38601232498698200100

Offset: 93

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 93..10000

Crossrefs

Cf. A017758, A017759, A017760, A001787, A242091.

Programs

Magma

[Binomial(n,93): n in [93..110]]; // G. C. Greubel, Nov 12 2018

Mathematica

Table[Binomial[n, 93], {n, 93, 120}] (* Vladimir Joseph Stephan Orlovsky, Jul 15 2011 *)

PARI

for(n=93, 110, print1(binomial(n,93), ", ")) \\ G. C. Greubel, Nov 12 2018

Sage

[binomial(n, 93) for n in range(93,108)] # Zerinvary Lajos, May 23 2009

Formula

From G. C. Greubel, Nov 12 2018: (Start)

G.f.: x^93/(1-x)^94.

E.g.f.: x^93*exp(x)/93!. (End)

From Amiram Eldar, Dec 20 2020: (Start)

Sum_{n>=93} 1/a(n) = 93/92.

Sum_{n>=93} (-1)^(n+1)/a(n) = A001787(93)*log(2) - A242091(93)/92! = 460513694614161462262474211328*log(2) - 154188882548936228348285592429207553818975770453922184600043633629 / 483042174022506354371285118995346300 = 0.9895789421... (End)