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%I #20 Nov 28 2023 14:28:16
%S 1,1,1,1,1,6,31,106,281,946,7561,54286,281161,1207636,7997991,
%T 81996916,701522641,4580581916,29742355441,306369616636,3632198902321,
%U 34977922146721,282526761829621,2720464688299821,36188717552636881,464906756446099276,4985291127563074901
%N E.g.f. satisfies A(x) = exp(x*A(x^4/4!)).
%H Alois P. Heinz, <a href="/A143568/b143568.txt">Table of n, a(n) for n = 0..525</a>
%F 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 A:= proc(n) option remember; if n<=0 then 1 else
%p unapply(convert(series(exp(x*A(n-4)(x^4/24)), x, n+1), polynom), x) fi
%p end:
%p a:= n-> coeff(A(n)(x), x,n)*n!:
%p seq(a(n), n=0..30);
%t 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 4th column of A143565.
%Y Cf. A367720.
%K nonn
%O 0,6
%A _Alois P. Heinz_, Aug 24 2008
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