The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #6 Feb 07 2026 16:00:40
%S 1,1,3,11,54,323,2241,17671,155755,1512825,16017287,183318386,
%T 2252439489,29539906896,411465894871,6061717452230,94103831065202,
%U 1534537091424337,26210557169790053,467745495221383190,8701568001160424952,168405853681337658542,3384457796699512302326
%N G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)^3) / (1 - x)^2.
%F a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n+2*k,n-k-1) * a(k).
%t nmax = 22; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - x)^3]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 2 k, n - k - 1] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 22}]
%Y Cf. A000110, A040027, A045501, A125273, A125274, A351813, A351816, A393227.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Feb 06 2026