OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..338
P. Laurens, Series development for the Laplace limit?, posting to sci.math, Sep 05 2002.
FORMULA
a(n) = n! * Sum_{k=0..n-1} (-1)^k*(2*n-k)*C(n-1, k)*(4*n)^k/(k+2)!
a(n) = n*n!*hypergeom([1-2*n,1-n],[3,-2*n],4*n). - Robert Israel, Jan 08 2018
MAPLE
f := n -> simplify(n!*n*hypergeom([-2*n+1, 1-n], [3, -2*n], 4*n)):
map(f, [$0..20]); # Robert Israel, Jan 08 2018
MATHEMATICA
Array[#*#!*HypergeometricPFQ[{1 - 2 #, 1 - #}, {3, -2 #}, 4 #] &, 15] (* Michael De Vlieger, Jan 09 2018 *)
PROG
(PARI) a(n) = n! * sum(k=0, n-1, (-1)^k*(2*n-k)*binomial(n-1, k)*(4*n)^k/(k+2)!) \\ Michel Marcus, Jul 26 2013
CROSSREFS
KEYWORD
sign
AUTHOR
Joe Keane (jgk(AT)jgk.org), Sep 06 2002
STATUS
approved