A098339 Expansion of 1/sqrt(1 - 6x + 17x^2).

1, 3, 5, -9, -111, -477, -1051, 1095, 21793, 106947, 276165, -71145, -4712655, -26071965, -76452315, -29748249, 1045547073, 6564746115, 21507513221, 19922192439, -230801512751, -1674387214173, -6072718662555

Offset

0,2

Comments

Binomial transform of A098336. Second binomial transform of A098332.

Central coefficients of (1 + 3x - 2x^2)^n.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..1628

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(3x)*BesselI(0, 2*sqrt(-2)*x).

D-finite with recurrence: n*a(n) + 3*(1-2*n)*a(n-1) + 17*(n-1)*a(n-2) = 0. - R. J. Mathar, Nov 09 2012

Mathematica

CoefficientList[Series[1/Sqrt[1-6x+17x^2], {x, 0, 30}], x] (* Harvey P. Dale, Jun 19 2013 *)

Crossrefs

Sequence in context: A215440 A163550 A123220 * A121622 A188983 A083519

Adjacent sequences: A098336 A098337 A098338 * A098340 A098341 A098342

Keyword

easy,sign

Author

Paul Barry, Sep 03 2004

Status

approved