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A017764 a(n) = binomial coefficient C(n,100). 2
1, 101, 5151, 176851, 4598126, 96560646, 1705904746, 26075972546, 352025629371, 4263421511271, 46897636623981, 473239787751081, 4416904685676756, 38393094575497956, 312629484400483356, 2396826047070372396, 17376988841260199871, 119594570260437846171 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=100..117.

FORMULA

G.f.: x^100/(1 - x)^101. - Ilya Gutkovskiy, Mar 21 2016

MATHEMATICA

Table[Binomial[n, 100], {n, 100, 5!}] (* Vladimir Joseph Stephan Orlovsky, Sep 25 2008 *)

PROG

(Sage) [binomial(n, 100) for n in xrange(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

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).

Sequence in context: A027900 A166218 A167626 * A217677 A152756 A265172

Adjacent sequences:  A017761 A017762 A017763 * A017765 A017766 A017767

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 24 00:42 EDT 2016. Contains 274964 sequences.