A351969 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n-1,4*k) * a(k) * a(n-4*k-1).

1, 1, 1, 1, 1, 2, 7, 22, 57, 128, 389, 1904, 9329, 38040, 132147, 542648, 3283633, 20997824, 114657097, 536178880, 2784500161, 19876061313, 153326461333, 1034551840125, 6051063487505, 38079448058864, 312420426286609, 2785055245002944, 22141255546319849

Offset: 0

Author

Ilya Gutkovskiy, Feb 26 2022

Keywords

• nonn

Crossrefs

Cf. A138314, A351968.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 4 k] a[k] a[n - 4 k - 1], {k, 0, Floor[(n - 1)/4]}]; Table[a[n], {n, 0, 28}]

Formula

E.g.f.: exp( Sum_{n>=0} a(n) * x^(4*n+1) / (4*n+1)! ).