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%I #6 Feb 19 2022 13:54:18
%S 1,1,1,1,1,1,3,7,15,31,63,129,277,651,1703,4859,14581,44711,138053,
%T 427709,1334461,4226501,13724063,46110643,161210421,586729441,
%U 2213187623,8591628435,34081480017,137398121611,561199251633,2320442726999,9722362801575
%N G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 * A(x/(1 - x)) / (1 - x)^2.
%F a(0) = ... = a(4) = 1; a(n) = Sum_{k=0..n-5} binomial(n-4,k+1) * a(k).
%t nmax = 32; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 + x^5 A[x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[n_] := a[n] = If[n < 5, 1, Sum[Binomial[n - 4, k + 1] a[k], {k, 0, n - 5}]]; Table[a[n], {n, 0, 32}]
%Y Cf. A040027, A210542, A351437, A351660, A351707, A351755.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, Feb 18 2022