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A006438 Expansion of e.g.f. 1/sqrt(1-8x+x^2). 0

%I #13 Jan 30 2020 21:29:14

%S 1,4,47,924,25449,901380,39024495,1996824060,117897243345,

%T 7889215807620,590030724668175,48773659291364700,4415782937120703225,

%U 434554886774113805700,46185660455230892170575,5272363854999057185869500,643381344417456140309438625

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

%F 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

%F a(n) ~ sqrt(2)*n^n/(sqrt(8*sqrt(15)-30)*exp(n)*(4-sqrt(15))^n). - _Vaclav Kotesovec_, Jun 27 2013

%p a:= n-> n! *coeff(series(1/sqrt(1-8*x+x^2), x, n+1), x, n):

%p seq (a(n), n=0..20); # _Alois P. Heinz_, Sep 12 2012

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

%K nonn

%O 0,2

%A _N. J. A. Sloane_.

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)