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

%I A143573 #15 Nov 29 2023 10:25:24
%S A143573 1,1,1,1,1,1,1,1,1,1,11,111,661,2861,10011,30031,80081,194481,437581,
%T A143573 1385671,20323161,294517861,2851708861,20461620411,117812647921,
%U A143573 572637720601,2430703053351,9228958338601,32965820988101,225123959060001,4466029537119151
%N A143573 E.g.f. satisfies A(x) = exp(x*A(x^9/9!)).
%H A143573 Alois P. Heinz, <a href="/A143573/b143573.txt">Table of n, a(n) for n = 0..200</a>
%F A143573 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
%p A143573 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);
%t A143573 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 *)
%Y A143573 9th column of A143565.
%K A143573 nonn
%O A143573 0,11
%A A143573 _Alois P. Heinz_, Aug 24 2008