OFFSET
100,2
COMMENTS
More generally, the ordinary generating function for the binomial coefficients C(n,k) is x^k/(1 - x)^(k+1). - Ilya Gutkovskiy, Mar 21 2016
LINKS
G. C. Greubel, Table of n, a(n) for n = 100..1100
FORMULA
G.f.: x^100/(1 - x)^101. - Ilya Gutkovskiy, Mar 21 2016
E.g.f.: x^100 * exp(x)/(100)!. - G. C. Greubel, Nov 24 2017
From Amiram Eldar, Dec 20 2020: (Start)
Sum_{n>=100} 1/a(n) = 100/99.
MATHEMATICA
Table[Binomial[n, 100], {n, 100, 5!}] (* Vladimir Joseph Stephan Orlovsky, Sep 25 2008 *)
PROG
(Sage) [binomial(n, 100) for n in range(100, 115)] # Zerinvary Lajos, May 23 2009
(PARI) a(n)=binomial(n, 100) \\ Charles R Greathouse IV, Jun 28 2012
(Python)
A017764_list, m = [], [1]*101
for _ in range(10**2):
A017764_list.append(m[-1])
for i in range(100):
m[i+1] += m[i] # Chai Wah Wu, Jan 24 2016
(Magma) [Binomial(n, 100): n in [100..130]]; // G. C. Greubel, Nov 24 2017
CROSSREFS
Cf. similar sequences of the binomial coefficients C(n,k): A000012 (k = 0), A001477 (k = 1), A000217 (k = 2), A000292 (k = 3), A000332 (k = 4), A000389 (k = 5), A000579-A000582 (k = 6..9) A001287 (k = 10), A001288 (k = 11), A010965-A011001 (k = 12..48), A017713-A017763 (k = 49..99), this sequence (k = 100).
KEYWORD
nonn,easy
AUTHOR
STATUS
approved