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%I #21 May 11 2013 07:59:29
%S 1,1,13,37,289,1201,7741,38053,227137,1207009,6995053,38591653,
%T 221446369,1245188881,7130897437,40516456357,232260610177,
%U 1327920945601,7627285093069,43787832627493,252042452907169,1451244932278129,8370001674641917,48303478743113893,279083099450496961
%N G.f. : 1/(1-2x-23x^2)^(1/2).
%C Central coefficient of (1+x+6x^2)^n.
%H Vincenzo Librandi, <a href="/A098265/b098265.txt">Table of n, a(n) for n = 0..300</a>
%H Tony D. Noe, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Noe/noe35.html">On the Divisibility of Generalized Central Trinomial Coefficients</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
%F E.g.f.: exp(x)*BesselI(0, 2*sqrt(6)x).
%F a(n) = sum{k=0..floor(n/2), binomial(n, k)*binomial(n-k, k)*6^k}.
%F a(n) = sum{k=0..floor(n/2), binomial(n, 2k)*binomial(2k, k)*6^k}.
%F n*a(n) +(1-2n)*a(n-1) +23(1-n)*a(n-2)=0. (Recurrence (4) in the Noe paper).- _Veka Gesell_, Jun 26 2012
%F a(n) ~ sqrt(72+6*sqrt(6))*(1+2*sqrt(6))^n/(12*sqrt(Pi*n)). - _Vaclav Kotesovec_, Oct 14 2012
%t Table[SeriesCoefficient[1/Sqrt[1-2*x-23*x^2],{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 14 2012 *)
%o (PARI) x='x+O('x^66); Vec(1/(1-2*x-23*x^2)^(1/2)) \\ _Joerg Arndt_, May 11 2013
%Y Cf. A084601, A084603, A084605, A098264.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Aug 31 2004
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