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%I #15 Nov 29 2023 11:44:31
%S 1,1,1,1,1,1,1,1,1,10,91,496,1981,6436,18019,45046,102961,328186,
%T 4375801,56951038,500352841,3276290746,17289324361,77309034166,
%U 302908144177,1104328093276,7519851360451,134741602227376,2095457847783301,23492070829121896
%N E.g.f. satisfies A(x) = exp(x*A(x^8/8!)).
%H Alois P. Heinz, <a href="/A143572/b143572.txt">Table of n, a(n) for n = 0..200</a>
%F a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/8)} (8*k+1) * a(k) * a(n-1-8*k) / (40320^k * k! * (n-1-8*k)!). - _Seiichi Manyama_, Nov 29 2023
%p A:= proc(n) option remember; if n<=0 then 1 else unapply (convert (series (exp (x*A(n-8)(x^8/40320)), x,n+1), polynom),x) fi end: a:= n-> coeff (A(n)(x), x,n)*n!: seq(a(n), n=0..35);
%t A[n_] := A[n] = If[n <= 0, 1&, Function[Normal[Series[Exp[y*A[n-2][y^8/8!]], {y, 0, n+1}] /. y -> #]]]; a[n_] := Coefficient[A[n][x], x, n]*n!; Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Feb 13 2014, after Maple *)
%Y 8th column of A143565.
%K nonn
%O 0,10
%A _Alois P. Heinz_, Aug 24 2008
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