A074768 Related to series for Laplace limit constant.

0, 1, -4, 42, -736, 18200, -582624, 22918672, -1069947904, 57826348416, -3551472064000, 244313618844416, -18609923667234816, 1554954961060953088, -141407678375562489856, 13904110871649987840000

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

Sequence in context: A156453 A327200 A259062 * A295763 A266526 A140055

Adjacent sequences: A074765 A074766 A074767 * A074769 A074770 A074771

Keyword

sign

Author

Joe Keane (jgk(AT)jgk.org), Sep 06 2002

Status

approved