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E.g.f. satisfies: A(x) = exp(x*A(((x+1)^9-1)/9)).
2

%I #11 Dec 20 2014 13:50:52

%S 1,1,3,40,829,26096,1216327,76192824,6123167801,615764308672,

%T 75666884850091,11126407433017944,1925795142055097557,

%U 387184416676122044032,89407267196505737775311,23480531627128442036603416,6953687155109949099972629873

%N E.g.f. satisfies: A(x) = exp(x*A(((x+1)^9-1)/9)).

%H Alois P. Heinz, <a href="/A143640/b143640.txt">Table of n, a(n) for n = 0..100</a>

%p A:= proc(n,k::nonnegint) option remember; if n<=0 or k=0 then 1 else A(n-1,k)(((x+1)^k-1)/k) fi; unapply(convert(series(exp(x*%), x,n+1), polynom), x) end: a:= n-> coeff(A(n,9)(x), x,n)*n!: seq(a(n), n=0..20);

%t A[n_, k_] := Module[{f}, f[x_] = If[n <= 0 || k == 0, 1, A[n-1, k][((x+1)^k-1)/k]]; Normal[Series[Exp[x*f[x]], { x, 0, n+1}]] /. x -> #]&; a[n_] := Coefficient[A[n, 9][x], x, n]*n!; Table[a[n], {n, 0, 21}] (* _Jean-François Alcover_, Feb 14 2014, after Maple *)

%Y Cf. 9th column of A143632.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 27 2008