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

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

Offset

0,1

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

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.

Mathematica

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

Prog

(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
(Magma) [6*Factorial(2*n)/(n+2): n in [0..20]]; // G. C. Greubel, May 03 2019
(Sage) [6*factorial(2*n)/(n+2) for n in (0..20)] # G. C. Greubel, May 03 2019
(GAP) List([0..20], n-> 6*Factorial(2*n)/(n+2)) # G. C. Greubel, May 03 2019

Crossrefs

Cf. A060593.

Sequence in context: A042891 A032835 A102920 * A376966 A013330 A274663

Adjacent sequences: A064332 A064333 A064334 * A064336 A064337 A064338

Keyword

nonn

Author

Karol A. Penson, Sep 13 2001

Status

approved