A141625 - OEIS

%I #7 Feb 14 2014 07:10:45

%S 1,1,3,16,121,1196,14593,211884,3564177,68088880,1454676641,

%T 34335669820,886637924569,24846347615792,750534094219393,

%U 24299661162891796,839155129170873505,30780528267862736320,1194857640269127135937

%N E.g.f. satisfies: A(x) = exp(x*A(sin(x))).

%H Alois P. Heinz, <a href="/A141625/b141625.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)(sin(x))), x,n+1), polynom),x) fi end; a:= n-> coeff (A(n)(x), x,n)*n!: seq (a(n), n=0..20);

%t A[n_] := A[n] = If[n == 0, 1, Normal[Series[Exp[x*A[n-1][Sin[x]]], {x, 0, n+1}]] /. x -> #]&; a[n_] := Coefficient[A[n][x], x, n]*n!; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Feb 14 2014, after Maple *)

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 24 2008