A024502 - OEIS

A024502

a(n) = floor(C(2n,n)/2^n).

1, 1, 1, 2, 4, 7, 14, 26, 50, 94, 180, 344, 660, 1269, 2448, 4733, 9171, 17804, 34618, 67415, 131460, 256661, 501656, 981501, 1922106, 3767329, 7389761, 14505829, 28493592, 56004648, 110142474, 216731966, 426691058, 840452084, 1656184990

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..34.

FORMULA

For n>0, a(n) = floor(A006882(2*n-1) / n!). - Alex Ratushnyak, Nov 28 2013

EXAMPLE

a(4) = floor(1*3*5*7 / (1*2*3*4)) = floor(35/8) = 4.

MATHEMATICA

Table[Floor[Binomial[2n, n]/2^n], {n, 0, 40}] (* Harvey P. Dale, Mar 07 2016 *)

PROG

(Python)

import math

for n in range(55): print(str(math.factorial(2*n)//(math.factorial(n)**2 * 2**n)), end=', ')

# Alex Ratushnyak, Nov 28 2013

(PARI) a(n)=binomial(2*n, n)>>n \\ Charles R Greathouse IV, Jul 19 2016

CROSSREFS

Cf. A006882.

Sequence in context: A076739 A017996 A287154 * A280254 A280917 A052535

Adjacent sequences: A024499 A024500 A024501 * A024503 A024504 A024505

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Benoit Cloitre, Jan 26 2002

STATUS

approved