A143634 E.g.f. satisfies: A(x) = exp(x*A(((x+1)^3-1)/3)).

1, 1, 3, 22, 253, 4256, 96727, 2828274, 102988937, 4553158024, 239618067211, 14775790894734, 1053758625896077, 85965003368491300, 7947211237328151167, 825821792546485330306, 95772123012223308982673

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. 3rd 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,3)(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, 3][x], x, n]*n!; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Feb 14 2014, after Maple *)