A065141 a(n) = (n+1)*2^n*(2*n)!.

1, 8, 288, 23040, 3225600, 696729600, 214592716800, 89270570188800, 48206107901952000, 32780153373327360000, 27404208220101672960000, 27623441885862486343680000, 33037636495491533667041280000, 46252691093688147133857792000000

Offset

0,2

Links

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

Formula

Integral representation as n-th moment of a positive function on a positive half-axis, in Maple notation: a(n)=int(x^n*1/8*exp(-1/(sqrt(2))*sqrt(x))*(x+sqrt(2)*sqrt(x))/x, x=0..infinity), n=0, 1...

Hypergeometric generating function, in Maple notation: exp(4*x)*(BesselI(0, 4*x)+4*x*BesselI(0, 4*x)+4*x*BesselI(1, 4*x)), i.e. a(0)=1 and a(n)= evalf(limit(n!^2*diff(exp(4*x)*(BesselI(0, 4*x)+4*x*BesselI(0, 4*x)+4*x*BesselI(1, 4*x)), x$n), x=0)), n=1, 2...

Mathematica

f[n_] := (n + 1)*2^n*(2*n)!; Array[f, 13, 0] (* Robert G. Wilson v, Jan 09 2018 *)

Prog

(PARI) { for (n=0, 100, write("b065141.txt", n, " ", (n + 1)*2^n*(2*n)!) ) } \\ Harry J. Smith, Oct 11 2009
(Magma) [(n+1)*2^n*Factorial(2*n): n in [0..20]]; // Vincenzo Librandi, Jan 13 2018

Crossrefs

Sequence in context: A254408 A132592 A034977 * A190840 A000842 A202559

Adjacent sequences: A065138 A065139 A065140 * A065142 A065143 A065144

Keyword

nonn

Author

Karol A. Penson, Oct 16 2001

Status

approved