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%I #10 Mar 10 2022 05:49:06
%S 1,9,67,477,3363,23741,168451,1202685,8641539,62470141,454164483,
%T 3319054333,24371503107,179736723453,1330803769347,9889323810813,
%U 73733148770307,551423090098173,4135500638060547
%N Fifth column of triangle A115193 (called C(1,2)).
%C Also one eighth of the fourth diagonal of triangle A115195, called Y(1,2).
%H G. C. Greubel, <a href="/A115202/b115202.txt">Table of n, a(n) for n = 0..500</a>
%F a(n)= A115195(3+n,1+n)/8, n>=0.
%F G.f.: (-1 + 3*x + (1- 5*x + 2*x^2)*c(2*x))/(4*(1+x)*x^3), with the o.g.f. c(x) of A000108 (Catalan).
%F a(n) = A115193(4+n,4), n>=0.
%F a(n) = (-1)^n*8^(n+2)*(binomial(1/2, n+3)*Hypergeometric2F1(1,n+5/2; n+4; -8) + 20*binomial(1/2, n+4)*Hypergeometric2F1(1,n+7/2; n+5; -8) + 32*binomial(1/2, n+5)*Hypergeometric2F1(1,n+9/2; n+6; -8)). - _G. C. Greubel_, Feb 04 2016
%F D-finite with recurrence (n+4)*a(n) +2*(-6*n-13)*a(n-1) +(29*n-10)*a(n-2) +2*(13*n+22)*a(n-3) +8*(-2*n+3)*a(n-4)=0. - _R. J. Mathar_, Mar 10 2022
%t f[n_] := SeriesCoefficient[(1 - 9*x + 14*x^2 - (1 - 5*x + 2*x^2) Sqrt[1 - 8*x])/(16*x^4*(1 + x)), {x, 0, n}];
%t Table[f[n], {n, 0, 50}] (* _G. C. Greubel_, Feb 04 2016 *)
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Feb 03 2006
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