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A098619 G.f. A(x) satisfies: A(x*G098618(x)) = G098618(x), where G098618 is the g.f. for A098618(n) = A007482(n)*Catalan(n).

%I A098619 #11 May 12 2013 03:04:09
%S A098619 1,3,13,51,213,867,3589,14739,60853,250563,1033605,4259571,17565909,
%T A098619 72412707,298586661,1231016019,5075753589,20927272323,86286346693,
%U A098619 355763629491,1466857936405,6047981701347,24936516122469,102815688922899,423920292507061,1747866711689283,7206641564551429
%N A098619 G.f. A(x) satisfies: A(x*G098618(x)) = G098618(x), where G098618 is the g.f. for A098618(n) = A007482(n)*Catalan(n).
%C A098619 G.f. satisfies: A(x) = x/(series reversion of x*G098618(x)), where G098618 is the g.f. for A098618 = {1*1,3*1,11*2,39*5,139*14,495*42,1763*132,...}.
%H A098619 Vincenzo Librandi, <a href="/A098619/b098619.txt">Table of n, a(n) for n = 0..300</a>
%F A098619 G.f.: (sqrt(1-8*x^2) + 3*x)/(1-17*x^2).
%F A098619 a(2*n+1) = 3*17^n.
%F A098619 Recurrence: n*a(n) = (25*n-24)*a(n-2) - 136*(n-3)*a(n-4). - _Vaclav Kotesovec_, Oct 29 2012
%t A098619 Flatten[{1,3,13,51,Table[17^(n/2)*(1/2+1/2*(-1)^n + 3/34*Sqrt[17]*(1-(-1)^n) + Sum[(-1)^j*(4/17 + Sum[Binomial[2*k-1,k-1]*2^(k+3)/ ((k+1)*17^(k+1)), {k,1,Floor[(j-1)/2]}]),{j,3,n-1}]),{n,4,20}]}] (* _Vaclav Kotesovec_, Oct 29 2012 *)
%o A098619 (PARI) a(n)=polcoeff((sqrt(1-8*x^2+x^2*O(x^n))+3*x)/(1-17*x^2),n);
%o A098619 (PARI) x='x+O('x^66); Vec((sqrt(1-8*x^2) + 3*x)/(1-17*x^2)) \\ _Joerg Arndt_, May 12 2013
%Y A098619 Cf. A098618, A098615, A098617, A007482, A000108.
%K A098619 nonn
%O A098619 0,2
%A A098619 _Paul D. Hanna_, Oct 14 2004