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%I #9 Mar 28 2018 21:59:55
%S 11,73,387,1876,8670,38907,171171,742456,3186378,13562770,57352526,
%T 241234488,1010195420,4214583135,17527709475,72695369520,300782736210,
%U 1241908383870,5118246664410,21058891783800,86518038936420,354975217564110,1454668818567822,5954594437631376,24350248227272100,99484144007729572
%N 4^n*(n+1)*(8*n^2+32*n+33)*P(3/2,n)/(3*P(4,n)) where P(a,n) is the Pochhammer rising factorial.
%H Robert Israel, <a href="/A217946/b217946.txt">Table of n, a(n) for n = 0..1654</a>
%H Ping Sun, <a href="http://dx.doi.org/10.1016/j.disc.2012.09.003">Proof of two conjectures of Petkovsek and Wilf on Gessel walks</a> Discrete Math. 312 (2012), no. 24, 3649--3655. MR2979494. See Th. 1.1, case 3.
%F From _Robert Israel_, Mar 28 2018: (Start)
%F (n+1)^2*(n+4)*(8*n^2+32*n+33)*a(n+1) = 2*(2*n+3)*(n+2)*(8*n^2+48*n+73)*a(n).
%F G.f.: (3-x)/(2*x^3) - (3-19*x+24*x^2-16*x^3)/(2*(1-4*x)^(3/2)*x^3). (End)
%p f:= n -> 4^n*(n+1)*(8*n^2+32*n+33)*pochhammer(3/2,n)/(3*pochhammer(4,n)):
%p map(f, [$0..40]); # _Robert Israel_, Mar 28 2018
%K nonn
%O 0,1
%A _N. J. A. Sloane_, Nov 07 2012