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%I #7 Feb 14 2014 07:51:24
%S 1,1,3,16,133,1496,21343,371064,7633641,181891072,4937228411,
%T 150669126400,5114378969965,191400122127488,7838565428874391,
%U 349073700821172736,16811407320683479633,871413633401197096960
%N E.g.f. satisfies: A(x) = exp(x*A(tan(x))).
%H Alois P. Heinz, <a href="/A141628/b141628.txt">Table of n, a(n) for n = 0..100</a>
%p A:= proc(n) option remember; if n=0 then 1 else unapply (convert (series (exp (x*A(n-1)(tan(x))), x,n+1), polynom),x) fi end: a:= n-> coeff (A(n)(x), x,n)*n!: seq (a(n), n=0..19);
%t A[n_] := A[n] = If[n == 0, 1, Normal[Series[Exp[x*A[n-1][Tan[x]]], {x, 0, n+1}]] /. x -> #]&; a[n_] := Coefficient[A[n][x], x, n]*n!; Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Feb 14 2014, after Maple *)
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 24 2008
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