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%I #5 Apr 10 2022 09:47:06
%S 1,1,2,3,4,6,12,28,64,137,282,583,1244,2733,6062,13343,28944,61969,
%T 131602,278483,588564,1242646,2618924,5505556,11542528,24142217,
%U 50409898,105154719,219278860,457362189,954629598,1994940799,4175986720,8760742945,18428667938
%N a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n,4*k+1) * a(k).
%F G.f. A(x) satisfies: A(x) = 1 + x * A(x^4/(1 - x)^4) / (1 - x)^2.
%F E.g.f.: 1 + exp(x) * Sum_{n>=0} a(n) * x^(4*n+1) / (4*n+1)!.
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 4 k + 1] a[k], {k, 0, Floor[(n - 1)/4]}]; Table[a[n], {n, 0, 34}]
%t nmax = 34; A[_] = 0; Do[A[x_] = 1 + x A[x^4/(1 - x)^4]/(1 - x)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]
%Y Cf. A040027, A119685, A352066, A352879.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Apr 07 2022