A017720 Binomial coefficients C(n,56).

1, 57, 1653, 32509, 487635, 5949147, 61474519, 553270671, 4426165368, 31966749880, 210980549208, 1285063345176, 7282025622664, 38650751381832, 193253756909160, 914734449370024, 4116305022165108, 17675898036356052

Offset: 56

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 56..10000

Crossrefs

Cf. A017717, A017719, A001787, A242091.

Programs

Magma

[Binomial(n,56): n in [56..80]]; // G. C. Greubel, Nov 03 2018

Mathematica

Table[Binomial[n,56],{n,56,80}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

PARI

for(n=56, 80, print1(binomial(n,56), ", ")) \\ G. C. Greubel, Nov 03 2018

Sage

[binomial(n, 56) for n in range(56,74)] # Zerinvary Lajos, May 23 2009

Formula

From G. C. Greubel, Nov 03 2018: (Start)

G.f.: x^56/(1-x)^57.

E.g.f.: x^56*exp(x)/56!. (End)

From Amiram Eldar, Dec 16 2020: (Start)

Sum_{n>=56} 1/a(n) = 56/55.

Sum_{n>=56} (-1)^n/a(n) = A001787(56)*log(2) - A242091(56)/55! = 2017612633061982208*log(2) - 41018417879588738008814416366926778496 / 29330242629471040257 = 0.9830322375... (End)