A115203 Sixth column of triangle A115193 (called C(1,2)).

1, 11, 93, 723, 5437, 40323, 297469, 2191875, 16164861, 119443459, 884719613, 6570430467, 48927031293, 365303660547, 2734459846653, 20518848036867, 154328140087293, 1163305103130627, 8787088644243453

Offset

0,2

Comments

Also fifth diagonal of triangle A115195, called Y(1,2), divided by 16.

Links

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

Formula

a(n) = A115195(4+n,1+n)/16, n>=0.

G.f.: (-1 + 5*x -2*x^2 + (1- 7*x + 8*x^2)*c(2*x))/(8*(1+x)*x^4) with the o.g.f. c(x) of A000108 (Catalan).

G.f. is also: ((1 + 2*x*c(2*x))*(2*x*c(2*x))^5)/(32*(1+x)*x^5).

a(n) = A115193(5+n,5), n>=0.

a(n) = (-1)^(n+1)* 2^(10 + 3*n)*(binomial(1/2,n+4)*Hypergeometric2F1(1, 7/2 + n, 5 + n, -8) + 7*binomial(1/2,n+5)*Hypergeometric2F1(1, 9/2 + n, 6 + n, -8) + 8*binomial(1/2,n+6)*Hypergeometric2F1(1, 11/2 + n, 7 + n, -8)). - G. C. Greubel, Feb 04 2016

a(n) ~ 2^(3*n+10) / (9*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Feb 05 2016

D-finite with recurrence (n+5)*a(n) +2*(-7*n-22)*a(n-1) +(49*n+43)*a(n-2) +124*a(n-3) +32*(-2*n+1)*a(n-4)=0. - R. J. Mathar, Mar 10 2022

Mathematica

f[n_] := SeriesCoefficient[(1 - 11*x + 28*x^2 - 8*x^3 - (1 - 7*x + 8*x^2) Sqrt[1 - 8*x])/(32*x^5*(1 + x)), {x, 0, n}];
Table[f[n], {n, 0, 50}] (* G. C. Greubel, Feb 04 2016 *)

Crossrefs

Cf. A000108, A115202, A115204.

Sequence in context: A025507 A081575 A016150 * A164547 A298925 A016203

Adjacent sequences: A115200 A115201 A115202 * A115204 A115205 A115206

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 03 2006

Status

approved