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%I #5 Mar 16 2022 16:33:06
%S 1,1,2,6,24,121,732,5166,41664,378002,3810532,42254256,511145184,
%T 6698543286,94536850576,1429503114816,23056734645504,395129481418584,
%U 7169760547544240,137325429039660432,2768685793537965504,58611883690279194361,1299873446056852916876
%N a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n,4*k+1) * a(k) * a(n-4*k-1).
%F E.g.f.: 1 / (1 - 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] a[n - 4 k - 1], {k, 0, Floor[(n - 1)/4]}]; Table[a[n], {n, 0, 22}]
%Y Cf. A351969, A352435, A352436.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Mar 16 2022