A064335 - OEIS

%I #17 Sep 08 2022 08:45:04

%S 3,4,36,864,40320,3110400,359251200,58118860800,12553673932800,

%T 3492203839488000,1216451004088320000,518769566666588160000,

%U 265906457885674045440000,161316584450642254233600000

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

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

%H Harry J. Smith, <a href="/A064335/b064335.txt">Table of n, a(n) for n = 0..100</a>

%F 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.

%t Table[6*(2*n)!/(n+2), {n,0,20}] (* _G. C. Greubel_, May 03 2019 *)

%o (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

%o (PARI) a(n) = 6*(2*n)!/(n+2); \\ _Michel Marcus_, Jun 24 2018

%o (Magma) [6*Factorial(2*n)/(n+2): n in [0..20]]; // _G. C. Greubel_, May 03 2019

%o (Sage) [6*factorial(2*n)/(n+2) for n in (0..20)] # _G. C. Greubel_, May 03 2019

%o (GAP) List([0..20], n-> 6*Factorial(2*n)/(n+2)) # _G. C. Greubel_, May 03 2019

%Y Cf. A060593.

%K nonn

%O 0,1

%A _Karol A. Penson_, Sep 13 2001