A294984 Number of compositions (ordered partitions) of 1 into exactly 5n+1 powers of 1/(n+1).

1, 525, 487630, 709097481, 1303699790001, 2713420774885145, 6078597035484932995, 14303426764164190428105, 34883776613634643730481238, 87451065686506297464527100009, 224099040671253218432160498959100, 584668421756097333754383886118155275

Offset: 0

Author

Alois P. Heinz, Nov 12 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..287

Crossrefs

Row n=5 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)))(5):
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]]&[5];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, May 21 2018, translated from Maple *)

Formula

a(n) ~ 5^(5*n + 3/2) / (4 * Pi^2 * n^2). - Vaclav Kotesovec, Sep 20 2019