A098442 Expansion of 1/sqrt(1-2x-95x^2).

1, 1, 49, 145, 3745, 17761, 329041, 2057329, 31209025, 232680385, 3110464369, 26033283409, 320766732001, 2899777798945, 33888636756625, 322631662569265, 3643305557364865, 35919365323430785, 396728681192463025

Offset

0,3

Comments

11th binomial transform of 2^n*LegendreP(n,-5) Binomial transform of 1/sqrt(1-96x^2).

Links

T. D. Noe, Table of n, a(n) for n = 0..100

Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.

Formula

a(n) = sum{k=0..floor(n/2), binomial(n-k, k)binomial(n, k)24^k}.

D-finite with recurrence: a(n+2) = ( (2*n+3)*a(n+1) + 95*(n+1)*a(n) )/(n+2); a(0)=a(1)=1. - Sergei N. Gladkovskii, Aug 01 2012

a(n) ~ sqrt(72+3*sqrt(6))*(1+4*sqrt(6))^n/(12*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 15 2012

Mathematica

CoefficientList[Series[1/Sqrt[1-2x-95x^2], {x, 0, 30}], x] (* Harvey P. Dale, Jan 18 2012 *)

Crossrefs

Sequence in context: A009404 A316121 A087354 * A088535 A045897 A162942

Adjacent sequences: A098439 A098440 A098441 * A098443 A098444 A098445

Keyword

easy,nonn

Author

Paul Barry, Sep 07 2004

Status

approved