A017755 Binomial coefficients C(n,91).

1, 92, 4278, 134044, 3183545, 61124064, 988172368, 13834413152, 171200862756, 1902231808400, 19212541264840, 178152655364880, 1529143625215220, 12233149001721760, 91748617512913200, 648356897091253280

Offset: 91

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 91..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,91): n in [91..110]]; // G. C. Greubel, Nov 12 2018

Mathematica

Binomial[Range[91,110],91] (* Harvey P. Dale, May 11 2013 *)

PARI

for(n=91, 110, print1(binomial(n,91), ", ")) \\ G. C. Greubel, Nov 12 2018

Sage

[binomial(n, 91) for n in range(91,107)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^91/(1-x)^92.

E.g.f.: x^91*exp(x)/91!. (End)

From Amiram Eldar, Dec 20 2020: (Start)

Sum_{n>=91} 1/a(n) = 91/90.

Sum_{n>=91} (-1)^(n+1)/a(n) = A001787(91)*log(2) - A242091(91)/90! = 112652543574969605015820304384*log(2) - 9636805159308514271767849526733246513466312934686984237288426594 / 123414621384871129001454714468591225 = 0.9893570273... (End)