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%I #7 Feb 07 2026 16:00:27
%S 1,1,4,15,68,365,2215,14917,110324,887232,7692852,71431239,706389705,
%T 7404870499,81949655191,954124880754,11650772679964,148804052320029,
%U 1983050788356644,27515009940760592,396709919909663826,5933004526233997409,91891268337714271137,1471741514111153388248
%N G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)^2) / (1 - x)^3.
%F a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n+k+1,n-k-1) * a(k).
%t nmax = 23; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - x)^2]/(1 - x)^3 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + k + 1, n - k - 1] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 23}]
%Y Cf. A000110, A040027, A045501, A125273, A125274, A351813, A351816, A393228.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Feb 06 2026