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A001449 Binomial coefficients binomial(5n,n). 5
1, 5, 45, 455, 4845, 53130, 593775, 6724520, 76904685, 886163135, 10272278170, 119653565850, 1399358844975, 16421073515280, 193253756909160, 2280012686716080, 26958221130508525 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

T. D. Noe, Table of n, a(n) for n = 0..100

FORMULA

a(n) = (5*n)!/((4*n)!*(n)!).

a(n) is asymptotic to c*(3125/256)^n/sqrt(n), with c = sqrt(5/(8*Pi)) = 0.44603102903819277863474159... - Benoit Cloitre, Jan 23 2008

a(n) = C(5*n-1,n-1)*C(25*n^2,2)/(3*n*C(5*n+1,3)), n>0. - Gary Detlefs, Jan 02 2014

G.f.: A(x) = x*B'(x)/B(x), where B(x)+1 is g.f. of A002294. - Vladimir Kruchinin, Oct 05 2015

From Ilya Gutkovskiy, Jan 16 2017: (Start)

O.g.f.: 4F3(1/5,2/5,3/5,4/5; 1/4,1/2,3/4; 3125*x/256).

E.g.f.: 4F4(1/5,2/5,3/5,4/5; 1/4,1/2,3/4,1; 3125*x/256). (End)

a(n) = hypergeom([-4*n, -n], [1], 1). - Peter Luschny, Mar 19 2018

MAPLE

f := n->(5*n)!/((4*n)!*(n)!);

MATHEMATICA

Table[ Binomial[5n, n], {n, 0, 18} ]

PROG

(MAGMA)[ Binomial(5*n, n): n in [0..100] ]; // Vincenzo Librandi, Apr 13 2011

(Maxima)

B(x):=sum(binomial(5*n, n-1)/n*x^n, n, 1, 30);

taylor(x*diff(B(x), x)/B(x), x, 0, 10); /* Vladimir Kruchinin, Oct 05 2015 */

(PARI) a(n) = binomial(5*n, n) \\ Altug Alkan, Oct 05 2015

CROSSREFS

Sequence in context: A054318 A093140 A137233 * A209442 A199753 A220877

Adjacent sequences:  A001446 A001447 A001448 * A001450 A001451 A001452

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 27 12:01 EST 2020. Contains 331295 sequences. (Running on oeis4.)