A352437 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n,4*k+1) * a(k) * a(n-4*k-1).
1, 1, 2, 6, 24, 121, 732, 5166, 41664, 378002, 3810532, 42254256, 511145184, 6698543286, 94536850576, 1429503114816, 23056734645504, 395129481418584, 7169760547544240, 137325429039660432, 2768685793537965504, 58611883690279194361, 1299873446056852916876
Offset: 0
Keywords
Programs
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Mathematica
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}]
Formula
E.g.f.: 1 / (1 - Sum_{n>=0} a(n) * x^(4*n+1) / (4*n+1)!).