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A143571 E.g.f. satisfies A(x) = exp(x*A(x^7/7!)).

%I A143571 #19 Nov 29 2023 11:44:14
%S A143571 1,1,1,1,1,1,1,1,9,73,361,1321,3961,10297,24025,77221,926641,10696401,
%T A143571 84365425,499445857,2395445521,9778915441,36584246161,248210675593,
%U A143571 3971313933049,54773770095001,549282704399001,4258482133019401,27025791550397641
%N A143571 E.g.f. satisfies A(x) = exp(x*A(x^7/7!)).
%H A143571 Alois P. Heinz, <a href="/A143571/b143571.txt">Table of n, a(n) for n = 0..566</a>
%F A143571 a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/7)} (7*k+1) * a(k) * a(n-1-7*k) / (5040^k * k! * (n-1-7*k)!). - _Seiichi Manyama_, Nov 29 2023
%p A143571 A:= proc(n) option remember; if n<=0 then 1 else unapply(convert(
%p A143571       series(exp(x*A(n-7)(x^7/5040)), x, n+1), polynom), x) fi
%p A143571     end:
%p A143571 a:= n-> coeff(A(n)(x), x,n)*n!:
%p A143571 seq(a(n), n=0..34);
%t A143571 A[n_] := A[n] = If[n <= 0, 1&, Function[Normal[Series[Exp[y*A[n-2][y^7/7!]], {y, 0, n+1}] /. y -> #]]]; a[n_] := Coefficient[A[n][x], x, n]*n!; Table[a[n], {n, 0, 34}] (* _Jean-François Alcover_, Feb 13 2014, after Maple *)
%Y A143571 7th column of A143565.
%K A143571 nonn
%O A143571 0,9
%A A143571 _Alois P. Heinz_, Aug 24 2008