A143570 E.g.f. satisfies A(x) = exp(x*A(x^6/6!)).

1, 1, 1, 1, 1, 1, 1, 8, 57, 253, 841, 2311, 5545, 18019, 192193, 1936936, 13533521, 71607537, 308979217, 1195354525, 8070684721, 113661781381, 1368278263969, 12100291273456, 83294670263113, 474179436692501, 2787857745272601, 32561274444909211

Offset: 0

Author

Alois P. Heinz, Aug 24 2008

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

6th column of A143565.

Programs

Maple

A:= proc(n) option remember; if n<=0 then 1 else unapply (convert (series (exp (x*A(n-6)(x^6/720)), x,n+1), polynom),x) fi end: a:= n-> coeff (A(n)(x), x,n)*n!: seq(a(n), n=0..33);

Mathematica

A[n_] := A[n] = If[n <= 0, 1&, Function[Normal[Series[Exp[y*A[n-2][y^6/6!]], {y, 0, n+1}] /. y -> #]]]; a[n_] := Coefficient[A[n][x], x, n]*n!; Table[a[n], {n, 0, 33}] (* Jean-François Alcover, Feb 13 2014, after Maple *)

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/6)} (6*k+1) * a(k) * a(n-1-6*k) / (720^k * k! * (n-1-6*k)!). - Seiichi Manyama, Nov 29 2023