A143571 E.g.f. satisfies A(x) = exp(x*A(x^7/7!)).

1, 1, 1, 1, 1, 1, 1, 1, 9, 73, 361, 1321, 3961, 10297, 24025, 77221, 926641, 10696401, 84365425, 499445857, 2395445521, 9778915441, 36584246161, 248210675593, 3971313933049, 54773770095001, 549282704399001, 4258482133019401, 27025791550397641

Offset

0,9

Links

Alois P. Heinz, Table of n, a(n) for n = 0..566

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/7)} (7*k+1) * a(k) * a(n-1-7*k) / (5040^k * k! * (n-1-7*k)!). - Seiichi Manyama, Nov 29 2023

Maple

A:= proc(n) option remember; if n<=0 then 1 else unapply(convert(
      series(exp(x*A(n-7)(x^7/5040)), x, n+1), polynom), x) fi
    end:
a:= n-> coeff(A(n)(x), x, n)*n!:
seq(a(n), n=0..34);

Mathematica

A[n_] := A[n] = If[n <= 0, 1&, Function[Normal[Series[Exp[y*A[n-2][y^7/7!]], {y, 0, n+1}] /. y -> #]]]; a[n_] := Coefficient[A[n][x], x, n]*n!; Table[a[n], {n, 0, 34}] (* Jean-François Alcover, Feb 13 2014, after Maple *)

Crossrefs

7th column of A143565.

Sequence in context: A096129 A365304 A291700 * A244202 A079927 A126641

Adjacent sequences: A143568 A143569 A143570 * A143572 A143573 A143574

Keyword

nonn

Author

Alois P. Heinz, Aug 24 2008

Status

approved