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

0,2

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

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A270913 A323266 A146279 * A086608 A291182 A037772

Adjacent sequences: A098616 A098617 A098618 * A098620 A098621 A098622

Keyword

nonn

Author

Paul D. Hanna, Oct 14 2004

Status

approved