A064335 a(n) = 6*(2*n)!/(n+2).

3, 4, 36, 864, 40320, 3110400, 359251200, 58118860800, 12553673932800, 3492203839488000, 1216451004088320000, 518769566666588160000, 265906457885674045440000, 161316584450642254233600000

Offset: 0

Author

Karol A. Penson, Sep 13 2001

Keywords

• nonn

Comments

All terms, except a(0) and a(1), are integer multiples of 6.

Links

• Harry J. Smith, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A060593.

Programs

GAP

List([0..20], n-> 6*Factorial(2*n)/(n+2)); # G. C. Greubel, May 03 2019

Magma

[6*Factorial(2*n)/(n+2): n in [0..20]]; // G. C. Greubel, May 03 2019

Mathematica

Table[6*(2*n)!/(n+2), {n,0,20}] (* G. C. Greubel, May 03 2019 *)

PARI

{ s=6; for (n=0, 100, if (n, s*=2*n*(2*n - 1)); a=s/(n + 2); write("b064335.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 12 2009

PARI

a(n) = 6*(2*n)!/(n+2); \\ Michel Marcus, Jun 24 2018

Sage

[6*factorial(2*n)/(n+2) for n in (0..20)] # G. C. Greubel, May 03 2019

Formula

a(n) = Integral_{x=0..oo} (x^n*(exp(-sqrt(x)) * (-1+sqrt(x)+2/sqrt(x)) + x*Ei(-sqrt(x))) ), n=0, 1..., where Ei(y) is the exponential integral. Representation as the n-th moment of a positive function on a positive half-axis, in Maple notation. This representation is unique.