A143639 - OEIS

%I #9 Dec 20 2014 13:50:01

%S 1,1,3,37,713,20931,900067,51768739,3815631297,351259985449,

%T 39429531406511,5287999813256799,833815716731955817,

%U 152569133029591977895,32033950906843181020467,7643291957710224206903131,2055010408602517321146955553,618032357523179035120686532401

%N E.g.f. satisfies: A(x) = exp(x*A(((x+1)^8-1)/8)).

%H Alois P. Heinz, <a href="/A143639/b143639.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,8)(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, 8][x], x, n]*n!; Table[a[n], {n, 0, 21}] (* _Jean-François Alcover_, Feb 14 2014, after Maple *)

%Y Cf. 8th column of A143632.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 27 2008