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%I #16 Jan 09 2019 21:23:10
%S 1,9,111,1785,35595,848925,23586255,748471185,26715409875,
%T 1059544210725,46230843633975,2201008238854425,113546715232225275,
%U 6309834090304870125,375777507964741257375,23876826206710426574625,1612323634555365676819875
%N Second column of triangle A000369: |S2(-3;n+2,2)|.
%H Robert Israel, <a href="/A143167/b143167.txt">Table of n, a(n) for n = 0..364</a>
%F a(n) = A000369(n+2,2) = |S2(-3;n+2,2)|, n >= 0.
%F E.g.f.: d^2/dx^2 ((1-(1-4*x)^(1/4))^2 )/2! = (3 - 2*(1-4*x)^(1/4))/(1-4*x)^(7/4).
%F From _Robert Israel_, Jan 09 2019: (Start)
%F a(n) = (8*n+1)*a(n-1) - 2*(4*n-1)*(2*n-1)*a(n-2).
%F a(n) = 4^(n+1)*(Gamma(n+7/4)/Gamma(3/4) - Gamma(n+3/2)/Gamma(1/2)). (End)
%p f:= gfun:-rectoproc({a(n) = (8*n+1)*a(n-1) - 2*(4*n-1)*(2*n-1)*a(n-2),a(0)=1, a(1)=9}, a(n), remember):
%p map(f, [$0..50]); # _Robert Israel_, Jan 09 2019
%o (PARI) x = 'x + O('x^40); serlaplace((3 - 2*(1-4*x)^(1/4))/(1-4*x)^(7/4)) \\ _Michel Marcus_, Jun 18 2017
%Y First column of A000369 is A008545, third one is A143168.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Sep 15 2008
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