A294988 Number of compositions (ordered partitions) of 1 into exactly 9n+1 powers of 1/(n+1).

1, 5259885, 121218250616173, 8684483842898500680225, 1085776473843765315524916060126, 179835209135492330050411858875313971595, 34994508245963099403565066291175900528344592700, 7565469782615095731665958935875509379368611893407583633

Offset: 0

Author

Alois P. Heinz, Nov 12 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..117

Crossrefs

Row n=9 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)))(9):
seq(a(n), n=0..10);

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]]&[9];
Table[a[n], {n, 0, 10}] (* Jean-François Alcover, May 21 2018, translated from Maple *)

Formula

a(n) ~ 9^(9*n + 3/2) / (16 * Pi^4 * n^4). - Vaclav Kotesovec, Sep 20 2019