A098460 Expansion of e.g.f. 1/sqrt(1-2x-2x^2).

1, 1, 5, 33, 321, 3945, 59445, 1056825, 21677985, 503799345, 13084021125, 375524312625, 11803392302625, 403235809601625, 14876913457531125, 589498927632239625, 24969077812488434625, 1125803018759825030625

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = (n!/2^n)*A084609(n);

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

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

D-finite with recurrence: a(n) +(1-2*n)*a(n-1) -2*(n-1)^2*a(n-2)=0. - R. J. Mathar, Nov 15 2011

a(n) ~ 2^(n+1/2)*n^n/(sqrt(3-sqrt(3))*exp(n)*(sqrt(3)-1)^n). - Vaclav Kotesovec, Jun 26 2013

Mathematica

CoefficientList[Series[1/Sqrt[1-2*x-2*x^2], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)

Prog

(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/sqrt(1-2*x-2*x^2))) \\ Michel Marcus, May 10 2020

Crossrefs

Cf. A012244.

Sequence in context: A001828 A084845 A198079 * A087618 A322178 A134152

Adjacent sequences: A098457 A098458 A098459 * A098461 A098462 A098463

Keyword

easy,nonn

Author

Paul Barry, Sep 08 2004

Status

approved