A370276 Self-convolution of A138020.

1, 4, 16, 72, 352, 1816, 9728, 53584, 301568, 1726488, 10022912, 58864240, 349102080, 2087772784, 12576358400, 76237953440, 464736354304, 2847019090712, 17518413479936, 108224749140784, 670996707147776, 4173817417204944, 26040046909915136, 162905940337309792, 1021700454913933312

Offset: 0

Author

Alexander Burstein, Feb 13 2024

Keywords

• nonn

Crossrefs

Cf. A138020, A000984.

Programs

Maple

A370276 := proc(n)
    add( A138020(i)*A138020(n-i),i=0..n) ;
end proc:
seq(A370276(n),n=0..80) ; # R. J. Mathar, Sep 27 2024

Mathematica

CoefficientList[(InverseSeries[Series[x Sqrt[(1-2x)/(1+2x)],{x,0,25}]])^2/x^2,x]

Formula

G.f.: A(x) = F(x)^2, where F(x) is the g.f. of A138020.

G.f.: (A(x)-1)/(A(x)+1) = 2*x*sqrt(A(x)) = 2*x*F(x).

G.f.: A(-x*A(x)) = 1/A(x).

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.

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