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

%I A143569 #15 Nov 29 2023 11:44:06
%S A143569 1,1,1,1,1,1,7,43,169,505,1261,4159,38809,334621,2036035,9489481,
%T A143569 38390353,257371297,3131783929,32230292725,246760346161,1493969858641,
%U A143569 9196517088991,101815213853431,1450104259874425,16645720979718601,147298665834676357
%N A143569 E.g.f. satisfies A(x) = exp(x*A(x^5/5!)).
%H A143569 Alois P. Heinz, <a href="/A143569/b143569.txt">Table of n, a(n) for n = 0..200</a>
%F A143569 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
%p A143569 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);
%t A143569 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 *)
%Y A143569 5th column of A143565.
%K A143569 nonn
%O A143569 0,7
%A A143569 _Alois P. Heinz_, Aug 24 2008