A349011 G.f. A(x) satisfies: A(x) = (1 - x * A(-x)) / (1 - 2 * x * A(x)).

1, 1, 5, 17, 105, 433, 2925, 13185, 93425, 443009, 3233205, 15840209, 117950745, 591187953, 4466545245, 22766535297, 173906505825, 897941153665, 6918379345125, 36089242700049, 279988660639305, 1472715584804529, 11490841104036045, 60857608450349313, 477104721264920145

Offset: 0

Author

Ilya Gutkovskiy, Nov 05 2021

Keywords

• nonn

Crossrefs

Cf. A001003, A103210, A348957.

Programs

Maple

A349011 := proc(n)
    option remember ;
    if n = 0 then
        1;
    else
        (-1)^n*procname(n-1)+2*add(procname(k)*procname(n-k-1),k=0..n-1) ;
    end if;
end proc:
seq(A349011(n),n=0..40) ; # R. J. Mathar, Aug 19 2022

Mathematica

nmax = 24; A[] = 0; Do[A[x] = (1 - x A[-x])/(1 - 2 x A[x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = (-1)^n a[n - 1] + 2 Sum[a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 24}]

Formula

a(0) = 1; a(n) = (-1)^n * a(n-1) + 2 * Sum_{k=0..n-1} a(k) * a(n-k-1).