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A074768
Related to series for Laplace limit constant.
1
0, 1, -4, 42, -736, 18200, -582624, 22918672, -1069947904, 57826348416, -3551472064000, 244313618844416, -18609923667234816, 1554954961060953088, -141407678375562489856, 13904110871649987840000
OFFSET
0,3
LINKS
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
Sequence in context: A156453 A327200 A259062 * A295763 A266526 A140055
KEYWORD
sign
AUTHOR
Joe Keane (jgk(AT)jgk.org), Sep 06 2002
STATUS
approved