OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..117
FORMULA
a(n) ~ 9^(9*n + 3/2) / (16 * Pi^4 * n^4). - Vaclav Kotesovec, Sep 20 2019
MAPLE
b:= proc(n, r, p, k) option remember;
`if`(n<r, 0, `if`(r=0, `if`(n=0, p!, 0), add(
b(n-j, k*(r-j), p+j, k)/j!, j=0..min(n, r))))
end:
a:= 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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 12 2017
STATUS
approved