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%I #19 Feb 16 2022 04:11:18
%S 1,1,1,5,16,46,142,496,1888,7538,31291,135739,617461,2939215,14575027,
%T 75014471,399901294,2205630124,12572140372,73961880118,448447331338,
%U 2798640572516,17956583819425,118336081817953,800278211629795,5549154792085813,39420390891260821
%N G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^4.
%F a(0) = a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n+1,k+3) * a(k).
%t nmax = 26; A[_] = 0; Do[A[x_] = 1 + x + x^2 A[x/(1 - x)]/(1 - x)^4 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n + 1, k + 3] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 26}]
%Y Cf. A007476, A045499, A351437, A351438.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Feb 12 2022