A081668 - OEIS

%I #11 Nov 19 2014 14:09:07

%S 1,2,2,2,6,2,20,2,70,2,252,2,924,2,3432,2,12870,2,48620,2,184756,2,

%T 705432,2,2704156,2,10400600,2,40116600,2,155117520,2,601080390,2,

%U 2333606220,2,9075135300,2,35345263800,2,137846528820,2,538257874440,2

%N Expansion of 2sinh(x) + BesselI_0(2x).

%C Binomial transform of A081668 is A081669.

%C a(n)-(1-(-1)^n) is the inverse binomial transform of the central trinomial coefficients A002426. - _N-E. Fahssi_, Jan 11 2008

%H Vincenzo Librandi, <a href="/A081668/b081668.txt">Table of n, a(n) for n = 0..1000</a>

%F E.g.f. 2sinh(x) + BesselI_0(2x)

%F G.f.: (2x)/(1 - x^2) + 1/Sqrt[1 - 4 x^2]. - _N-E. Fahssi_, Jan 11 2008

%F If n is even, a(n) ~ 2^(n+1/2) / sqrt(Pi*n). - _Vaclav Kotesovec_, Feb 12 2014

%t CoefficientList[Series[2*Sinh[x] + BesselI[0,2*x],{x,0,20}],x]*Range[0,20]! (* _Vaclav Kotesovec_, Feb 12 2014 *)

%Y Cf. A000984 (bisection).

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 28 2003