A294985 Number of compositions (ordered partitions) of 1 into exactly 6n+1 powers of 1/(n+1).

1, 4347, 40647178, 701954099115, 16596702491586251, 461871979542736134676, 14138484434475011392912026, 460977928965130046448503507051, 15732393344641740454307566725567376, 556054452693724489326948624520266970011, 20208669423838553069878798723999482271266772

Offset: 0

Author

Alois P. Heinz, Nov 12 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..215

Crossrefs

Row n=6 of A294746.

Programs

Maple

b:= proc(n, r, p, k) option remember;
      `if`(n (k-> `if`(n=0, 1, b(k*n+1, 1, 0, n+1)))(6):
seq(a(n), n=0..15);

Mathematica

b[n_, r_, p_, k_] := b[n, r, p, k] = If[n < r, 0, If[r == 0, If[n == 0, p!, 0], Sum[b[n - j, k*(r - j), p + j, k]/j!, {j, 0, Min[n, r]}]]];
a[n_] := If[n == 0, 1, b[#*n + 1, 1, 0, n + 1]]&[6];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, May 21 2018, translated from Maple *)

Formula

a(n) ~ 6^(6*n + 3/2) / (2*Pi*n)^(5/2). - Vaclav Kotesovec, Sep 20 2019