A345104 a(n) = 1 + 2 * Sum_{k=0..n-1} binomial(n-1,k) * a(k) * a(n-k-1).

1, 3, 13, 89, 825, 9601, 134185, 2188353, 40788745, 855303265, 19927758377, 510728051073, 14279388168137, 432505475357729, 14107767947949289, 493046896702987841, 18380057918926012809, 728005164671113691105, 30531323352522247757225, 1351567976217998536472833

Offset: 0

Author

Ilya Gutkovskiy, Jun 08 2021

Keywords

• nonn

Crossrefs

Cf. A000165, A052886, A054687, A345105.

Programs

Mathematica

a[n_] := a[n] = 1 + 2 Sum[Binomial[n - 1, k] a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 19}]
nmax = 19; A[] = 1; Do[A[x] = Normal[Integrate[2 A[x]^2 + Exp[x], x] + O[x]^(nmax + 1)], nmax]; CoefficientList[A[x], x] Range[0, nmax]!

Formula

E.g.f. A(x) satisfies: A'(x) = 2 * A(x)^2 + exp(x).