A143633 E.g.f. satisfies: A(x) = exp(x*A(((x+1)^2-1)/2)).

1, 1, 3, 19, 185, 2541, 45787, 1037359, 28649553, 942585625, 36294146171, 1612599520599, 81729515092777, 4679679856932133, 300257015404355115, 21436580394615666991, 1692530428442960006753, 146987828523665177048241

Offset: 0

Author

Alois P. Heinz, Aug 27 2008

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100

Crossrefs

Cf. 2nd column of A143632.

Programs

Maple

A:= proc(n,k::nonnegint) option remember; if n<=0 or k=0 then 1 else A(n-1,k)(((x+1)^k-1)/k) fi; unapply(convert(series(exp (x*%), x,n+1), polynom), x) end: a:= n-> coeff(A(n,2)(x), x,n)*n!: seq(a(n), n=0..21);

Mathematica

A[n_, k_] := Module[{f}, f[x_] = If[n <= 0 || k == 0, 1, A[n-1, k][((x+1)^k-1)/k]]; Normal[Series[Exp[x*f[x]], { x, 0, n+1}]] /. x -> #]&; a[n_] := Coefficient[A[n, 2][x], x, n]*n!; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Feb 14 2014, after Maple *)