A143573 E.g.f. satisfies A(x) = exp(x*A(x^9/9!)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 111, 661, 2861, 10011, 30031, 80081, 194481, 437581, 1385671, 20323161, 294517861, 2851708861, 20461620411, 117812647921, 572637720601, 2430703053351, 9228958338601, 32965820988101, 225123959060001, 4466029537119151

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

9th column of A143565.

Programs

Maple

A:= proc(n) option remember; if n<=0 then 1 else unapply (convert (series (exp (x*A(n-9)(x^9/362880)), x,n+1), polynom),x) fi end: a:= n-> coeff (A(n)(x), x,n)*n!: seq(a(n), n=0..36);

Mathematica

A[n_] := A[n] = If[n <= 0, 1&, Function[Normal[Series[Exp[y*A[n-2][y^9/9!]], {y, 0, n+1}] /. y -> #]]]; a[n_] := Coefficient[A[n][x], x, n]*n!; Table[a[n], {n, 0, 36}] (* Jean-François Alcover, Feb 13 2014, after Maple *)

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/9)} (9*k+1) * a(k) * a(n-1-9*k) / (362880^k * k! * (n-1-9*k)!). - Seiichi Manyama, Nov 29 2023