A006587 a(n) = 3*2^(2*n)*(3*n)!/((2*n)!*n!).

3, 36, 720, 16128, 380160, 9225216, 228114432, 5715394560, 144599482368, 3685869158400, 94513444945920, 2435255516528640, 62999001405849600, 1635260233414606848, 42568679092062781440, 1110895735754245275648

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• changed

References

• W. A. Whitworth, DCC Exercises in Choice and Chance, Stechert, NY, 1945, p. 35.

Links

• Delbert L. Johnson, Table of n, a(n) for n = 0..699
• M. Le Brun, Email to N. J. A. Sloane, Jul 1991

Crossrefs

Cf. A006588.

Programs

Magma

A006587:= func< n | 3*4^n*Binomial(3*n,n) >;
[A006587(n): n in [0..40]]; // G. C. Greubel, Aug 27 2025

Maple

A006587:=n->3*2^(2*n)*(3*n)!/((2*n)!*n!); seq(A006587(n), n=0..50); # Wesley Ivan Hurt, Nov 23 2013

Mathematica

Table[3*2^(2n)(3n)!/((2n)!*n!), {n, 0, 50}] (* Wesley Ivan Hurt, Nov 23 2013 *)

PARI

a(n)=3*binomial(3*n,n)*4^n \\ Charles R Greathouse IV, Aug 11 2017

SageMath

def A006587(n): return 3*4**n*binomial(3*n,n)
print([A006587(n) for n in range(41)]) # G. C. Greubel, Aug 27 2025

Formula

From G. C. Greubel, Aug 27 2025: (Start)

a(n) = 3 * A006588(n).

G.f.: 3*hypergeometric2F1([1/3, 2/3], [1/2], 27*x) = (3/(2*(1-27*x))*( cos(t) + cos(2*t) ), where t = (1/3)*arccos(1-54*x).

E.g.f.: 3*hypergeometric2F2([1/3, 2/3], [1/2, 1], 27*x). (End)