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%I #15 Sep 27 2024 06:27:30
%S 1,4,16,72,352,1816,9728,53584,301568,1726488,10022912,58864240,
%T 349102080,2087772784,12576358400,76237953440,464736354304,
%U 2847019090712,17518413479936,108224749140784,670996707147776,4173817417204944,26040046909915136,162905940337309792,1021700454913933312
%N Self-convolution of A138020.
%F G.f.: A(x) = F(x)^2, where F(x) is the g.f. of A138020.
%F G.f.: (A(x)-1)/(A(x)+1) = 2*x*sqrt(A(x)) = 2*x*F(x).
%F G.f.: A(-x*A(x)) = 1/A(x).
%F G.f.: A(x) = 1 + 4*x*A(x)*B(x^2*A(x)), where B(x) is the g.f. of the central binomial coefficients A000984.
%F D-finite with recurrence (n-1)*(n+2)*(5*n-12)*a(n) +4*(-55*n^3+242*n^2-316*n+120)*a(n-2) -16*(n-3)*(n-4)*(5*n-2)*a(n-4)=0. - _R. J. Mathar_, Sep 27 2024
%p A370276 := proc(n)
%p add( A138020(i)*A138020(n-i),i=0..n) ;
%p end proc:
%p seq(A370276(n),n=0..80) ; # _R. J. Mathar_, Sep 27 2024
%t CoefficientList[(InverseSeries[Series[x Sqrt[(1-2x)/(1+2x)],{x,0,25}]])^2/x^2,x]
%Y Cf. A138020, A000984.
%K nonn
%O 0,2
%A _Alexander Burstein_, Feb 13 2024