A098439 Expansion of 1/sqrt(1-2x-47x^2).

1, 1, 25, 73, 1009, 4561, 47881, 272665, 2480353, 16076449, 135464185, 945516265, 7648488145, 55729490545, 441280178665, 3297808663993, 25833412158913, 196026748033345, 1527879583118809, 11703693337452937, 91042025394288049

Offset

0,3

Comments

Binomial transform of 1/sqrt(1-48x^2).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Hacène Belbachir, Abdelghani Mehdaoui, László Szalay, Diagonal Sums in the Pascal Pyramid, II: Applications, J. Int. Seq., Vol. 22 (2019), Article 19.3.5.

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

Formula

E.g.f.: exp(x)*BesselI(0, 4*sqrt(3)*x).

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)*binomial(n, k)*12^k.

D-finite with recurrence: n*a(n) +(1-2*n)*a(n-1) +47*(1-n)*a(n-2)=0. - R. J. Mathar, Sep 26 2012

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

Mathematica

Table[SeriesCoefficient[1/Sqrt[1-2*x-47*x^2], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 15 2012 *)

Prog

(PARI) x='x+O('x^66); Vec(1/sqrt(1-16*x+48*x^2)) \\ Joerg Arndt, May 11 2013

Crossrefs

Sequence in context: A124718 A126379 A114553 * A318643 A044163 A044544

Adjacent sequences: A098436 A098437 A098438 * A098440 A098441 A098442

Keyword

easy,nonn

Author

Paul Barry, Sep 07 2004

Status

approved