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
KEYWORD
nonn
AUTHOR
Karol A. Penson, Oct 16 2001
STATUS
approved