A115202 Fifth column of triangle A115193 (called C(1,2)).

1, 9, 67, 477, 3363, 23741, 168451, 1202685, 8641539, 62470141, 454164483, 3319054333, 24371503107, 179736723453, 1330803769347, 9889323810813, 73733148770307, 551423090098173, 4135500638060547

Offset

0,2

Comments

Also one eighth of the fourth diagonal of triangle A115195, called Y(1,2).

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Formula

a(n)= A115195(3+n,1+n)/8, n>=0.

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).

a(n) = A115193(4+n,4), n>=0.

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

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

Mathematica

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}];
Table[f[n], {n, 0, 50}] (* G. C. Greubel, Feb 04 2016 *)

Crossrefs

Sequence in context: A105287 A163349 A016130 * A287817 A155592 A002051

Adjacent sequences: A115199 A115200 A115201 * A115203 A115204 A115205

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 03 2006

Status

approved