A074768 - OEIS

%I #16 Jan 10 2018 03:06:54

%S 0,1,-4,42,-736,18200,-582624,22918672,-1069947904,57826348416,

%T -3551472064000,244313618844416,-18609923667234816,

%U 1554954961060953088,-141407678375562489856,13904110871649987840000

%N Related to series for Laplace limit constant.

%H Robert Israel, <a href="/A074768/b074768.txt">Table of n, a(n) for n = 0..338</a>

%H P. Laurens, <a href="https://groups.google.com/forum/?hl=en#!topic/sci.math/usVJOw1teLw">Series development for the Laplace limit?</a>, posting to sci.math, Sep 05 2002.

%F a(n) = n! * Sum_{k=0..n-1} (-1)^k*(2*n-k)*C(n-1, k)*(4*n)^k/(k+2)!

%F a(n) = n*n!*hypergeom([1-2*n,1-n],[3,-2*n],4*n). - _Robert Israel_, Jan 08 2018

%p f := n -> simplify(n!*n*hypergeom([-2*n+1, 1-n], [3, -2*n], 4*n)):

%p map(f, [$0..20]); # _Robert Israel_, Jan 08 2018

%t Array[#*#!*HypergeometricPFQ[{1 - 2 #, 1 - #}, {3, -2 #}, 4 #] &, 15] (* _Michael De Vlieger_, Jan 09 2018 *)

%o (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

%K sign

%O 0,3

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