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

0,2

Links

Table of n, a(n) for n=0..24.

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

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]

Crossrefs

Cf. A138020, A000984.

Sequence in context: A151246 A152807 A217461 * A129872 A059371 A208528

Adjacent sequences: A370273 A370274 A370275 * A370277 A370278 A370279

Keyword

nonn

Author

Alexander Burstein, Feb 13 2024

Status

approved