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A143570 E.g.f. satisfies A(x) = exp(x*A(x^6/6!)).

%I A143570 #15 Nov 29 2023 11:44:10
%S A143570 1,1,1,1,1,1,1,8,57,253,841,2311,5545,18019,192193,1936936,13533521,
%T A143570 71607537,308979217,1195354525,8070684721,113661781381,1368278263969,
%U A143570 12100291273456,83294670263113,474179436692501,2787857745272601,32561274444909211
%N A143570 E.g.f. satisfies A(x) = exp(x*A(x^6/6!)).
%H A143570 Alois P. Heinz, <a href="/A143570/b143570.txt">Table of n, a(n) for n = 0..200</a>
%F A143570 a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/6)} (6*k+1) * a(k) * a(n-1-6*k) / (720^k * k! * (n-1-6*k)!). - _Seiichi Manyama_, Nov 29 2023
%p A143570 A:= proc(n) option remember; if n<=0 then 1 else unapply (convert (series (exp (x*A(n-6)(x^6/720)), x,n+1), polynom),x) fi end: a:= n-> coeff (A(n)(x), x,n)*n!: seq(a(n), n=0..33);
%t A143570 A[n_] := A[n] = If[n <= 0, 1&, Function[Normal[Series[Exp[y*A[n-2][y^6/6!]], {y, 0, n+1}] /. y -> #]]]; a[n_] := Coefficient[A[n][x], x, n]*n!; Table[a[n], {n, 0, 33}] (* _Jean-François Alcover_, Feb 13 2014, after Maple *)
%Y A143570 6th column of A143565.
%K A143570 nonn
%O A143570 0,8
%A A143570 _Alois P. Heinz_, Aug 24 2008