A143566 E.g.f. satisfies A(x) = exp(x*A(x^2/2!)).

1, 1, 1, 4, 13, 46, 241, 1471, 9409, 67348, 564841, 4771801, 45459481, 463867834, 5060656693, 58878140686, 730612429681, 9556314730456, 131627520296929, 1912237000523623, 29032781640572881, 462811831018070206, 7687624300327129621, 133275225843052767244

Offset: 0

Author

Alois P. Heinz, Aug 24 2008

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..480

Crossrefs

2nd column of A143565.

Cf. A138292.

Programs

Maple

A:= proc(n) option remember; if n<=0 then 1 else unapply(convert(
       series(exp(x*A(n-2)(x^2/2)), x,n+1), polynom),x) fi
    end:
a:= n-> coeff(A(n)(x), x,n)*n!:
seq(a(n), n=0..28);

Mathematica

A[n_] := A[n] = If[n <= 0, 1&, Function[Normal[Series[Exp[y*A[n-2][y^2/2]], {y, 0, n+1}] /. y -> #]]]; a[n_] := Coefficient[A[n][x], x, n]*n!; Table[a[n], {n, 0, 28}] (* Jean-François Alcover, Feb 13 2014, after Maple *)

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/2)} (2*k+1) * a(k) * a(n-1-2*k) / (2^k * k! * (n-1-2*k)!). - Seiichi Manyama, Nov 28 2023