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A143568 E.g.f. satisfies A(x) = exp(x*A(x^4/4!)).

%I A143568 #20 Nov 28 2023 14:28:16
%S A143568 1,1,1,1,1,6,31,106,281,946,7561,54286,281161,1207636,7997991,
%T A143568 81996916,701522641,4580581916,29742355441,306369616636,3632198902321,
%U A143568 34977922146721,282526761829621,2720464688299821,36188717552636881,464906756446099276,4985291127563074901
%N A143568 E.g.f. satisfies A(x) = exp(x*A(x^4/4!)).
%H A143568 Alois P. Heinz, <a href="/A143568/b143568.txt">Table of n, a(n) for n = 0..525</a>
%F A143568 a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/4)} (4*k+1) * a(k) * a(n-1-4*k) / (24^k * k! * (n-1-4*k)!). - _Seiichi Manyama_, Nov 28 2023
%p A143568 A:= proc(n) option remember; if n<=0 then 1 else
%p A143568       unapply(convert(series(exp(x*A(n-4)(x^4/24)), x, n+1), polynom), x) fi
%p A143568     end:
%p A143568 a:= n-> coeff(A(n)(x), x,n)*n!:
%p A143568 seq(a(n), n=0..30);
%t A143568 A[n_] := A[n] = If[n <= 0, 1&, Function[Normal[Series[Exp[y*A[n-2][y^4/4!]], {y, 0, n+1}] /. y -> #]]]; a[n_] := Coefficient[A[n][x], x, n]*n!; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Feb 13 2014, after Maple *)
%Y A143568 4th column of A143565.
%Y A143568 Cf. A367720.
%K A143568 nonn
%O A143568 0,6
%A A143568 _Alois P. Heinz_, Aug 24 2008