A143569 E.g.f. satisfies A(x) = exp(x*A(x^5/5!)).

1, 1, 1, 1, 1, 1, 7, 43, 169, 505, 1261, 4159, 38809, 334621, 2036035, 9489481, 38390353, 257371297, 3131783929, 32230292725, 246760346161, 1493969858641, 9196517088991, 101815213853431, 1450104259874425, 16645720979718601, 147298665834676357

Offset: 0

Author

Alois P. Heinz, Aug 24 2008

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

5th column of A143565.

Programs

Maple

A:= proc(n) option remember; if n<=0 then 1 else unapply (convert (series (exp (x*A(n-5)(x^5/120)), x,n+1), polynom),x) fi end: a:= n-> coeff (A(n)(x), x,n)*n!: seq(a(n), n=0..31);

Mathematica

A[n_] := A[n] = If[n <= 0, 1&, Function[Normal[Series[Exp[y*A[n-2][y^5/5!]], {y, 0, n+1}] /. y -> #]]]; a[n_] := Coefficient[A[n][x], x, n]*n!; Table[a[n], {n, 0, 31}] (* Jean-François Alcover, Feb 13 2014, after Maple *)

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/5)} (5*k+1) * a(k) * a(n-1-5*k) / (120^k * k! * (n-1-5*k)!). - Seiichi Manyama, Nov 29 2023