A006438 Expansion of e.g.f. 1/sqrt(1-8x+x^2).

1, 4, 47, 924, 25449, 901380, 39024495, 1996824060, 117897243345, 7889215807620, 590030724668175, 48773659291364700, 4415782937120703225, 434554886774113805700, 46185660455230892170575, 5272363854999057185869500, 643381344417456140309438625

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

D-finite with recurrence: a(n+2) = 4*(2*n+3)*a(n+1) -(n+1)^2*a(n); a(0)=1, a(1)=4. - Sergei N. Gladkovskii, Sep 12 2012

a(n) ~ sqrt(2)*n^n/(sqrt(8*sqrt(15)-30)*exp(n)*(4-sqrt(15))^n). - Vaclav Kotesovec, Jun 27 2013

Maple

a:= n-> n! *coeff(series(1/sqrt(1-8*x+x^2), x, n+1), x, n):
seq (a(n), n=0..20);  # Alois P. Heinz, Sep 12 2012

Mathematica

CoefficientList[Series[1/Sqrt[1-8*x+x^2], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)

Crossrefs

Sequence in context: A354405 A326434 A319833 * A251665 A210828 A361560

Adjacent sequences: A006435 A006436 A006437 * A006439 A006440 A006441

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved