A294987 Number of compositions (ordered partitions) of 1 into exactly 8n+1 powers of 1/(n+1).

1, 441675, 663134389930, 2594884910993019575, 16336038155342083651640376, 130958058407369286623026190867082, 1206534243283932582765850205674424343577, 12176825528022093702548525617184407475359333407, 131223281654667714701311635640432890136981994039662720

Offset: 0

Author

Alois P. Heinz, Nov 12 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..139

Crossrefs

Row n=8 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)))(8):
seq(a(n), n=0..12);

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]]&[8];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, May 21 2018, translated from Maple *)

Formula

a(n) ~ 8^(8*n + 3/2) / (2*Pi*n)^(7/2). - Vaclav Kotesovec, Sep 20 2019