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%I #9 Dec 20 2014 13:48:32
%S 1,1,3,31,505,12521,443227,20766159,1240975409,92068494625,
%T 8282460205891,886498379552919,111190541933344777,
%U 16136424098890466281,2680205744964849259355,504746978220729054647911,106901213223866930807470433,25280598116469824339521406081
%N E.g.f. satisfies: A(x) = exp(x*A(((x+1)^6-1)/6)).
%H Alois P. Heinz, <a href="/A143637/b143637.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,6)(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, 6][x], x, n]*n!; Table[a[n], {n, 0, 21}] (* _Jean-François Alcover_, Feb 14 2014, after Maple *)
%Y Cf. 6th column of A143632.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 27 2008
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