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).

1, 3, 13, 51, 213, 867, 3589, 14739, 60853, 250563, 1033605, 4259571, 17565909, 72412707, 298586661, 1231016019, 5075753589, 20927272323, 86286346693, 355763629491, 1466857936405, 6047981701347, 24936516122469, 102815688922899, 423920292507061, 1747866711689283, 7206641564551429

Offset: 0

Author

Paul D. Hanna, Oct 14 2004

Keywords

• nonn

Comments

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,...}.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A098618, A098615, A098617, A007482, A000108.

Programs

Mathematica

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 *)

PARI

a(n)=polcoeff((sqrt(1-8*x^2+x^2*O(x^n))+3*x)/(1-17*x^2),n);

PARI

x='x+O('x^66); Vec((sqrt(1-8*x^2) + 3*x)/(1-17*x^2)) \\ Joerg Arndt, May 12 2013

Formula

G.f.: (sqrt(1-8*x^2) + 3*x)/(1-17*x^2).

a(2*n+1) = 3*17^n.

Recurrence: n*a(n) = (25*n-24)*a(n-2) - 136*(n-3)*a(n-4). - Vaclav Kotesovec, Oct 29 2012