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

1, 1, 1, 1, 1, 6, 31, 106, 281, 946, 7561, 54286, 281161, 1207636, 7997991, 81996916, 701522641, 4580581916, 29742355441, 306369616636, 3632198902321, 34977922146721, 282526761829621, 2720464688299821, 36188717552636881, 464906756446099276, 4985291127563074901

Offset: 0

Author

Alois P. Heinz, Aug 24 2008

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..525

Crossrefs

4th column of A143565.

Cf. A367720.

Programs

Maple

A:= proc(n) option remember; if n<=0 then 1 else
      unapply(convert(series(exp(x*A(n-4)(x^4/24)), x, n+1), polynom), x) fi
    end:
a:= n-> coeff(A(n)(x), x,n)*n!:
seq(a(n), n=0..30);

Mathematica

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 *)

Formula

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