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%I #7 Aug 22 2012 12:06:41
%S 0,1,3,3,3,11,63,43,-837,171,34023,683,-1800477,2731,132912783,10923,
%T -12927652917,43691,1603253204343,174763,-246914125142157,699051,
%U 46232582930156703,2796203,-10343022775699132197,11184811,2724715006195438297863,44739243,-834839760935753154167037
%N E.g.f. (1/cosh(x)+tanh(x))*(exp(2*x)-exp(-x))/3.
%C A transform of the Jacobsthal numbers.
%C a(2n)=A007583(n)=(2*4^n+1)/3.
%t With[{nn=30},CoefficientList[Series[(1/Cosh[x]+Tanh[x]) (Exp[2x]- Exp[-x])/3, {x,0,nn}],x]Range[0,nn]!] (* _Harvey P. Dale_, Aug 22 2012 *)
%Y Cf. A101473, A001045.
%K easy,sign
%O 0,3
%A _Paul Barry_, Jan 21 2005
%E Corrected by _N. J. A. Sloane_, Nov 05 2005