OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..100
FORMULA
a(n) = A327673(2n,n).
MAPLE
b:= proc(n, i, k, p) option remember;
`if`(n=0, p!, `if`(i<1, 0, add(binomial(k^i, j)*
b(n-i*j, min(n-i*j, i-1), k, p+j)/j!, j=0..n/i)))
end:
a:= n-> add(b(2*n$2, i, 0)*(-1)^(n-i)*binomial(n, i), i=0..n):
seq(a(n), n=0..15);
MATHEMATICA
b[n_, i_, k_, p_] := b[n, i, k, p] =
If[n == 0, p!, If[i < 1, 0, Sum[Binomial[k^i, j]*
b[n - i*j, Min[n - i*j, i - 1], k, p + j]/j!, {j, 0, n/i}]]];
a[n_] := Sum[b[2n, 2n, i, 0]*(-1)^(n-i)*Binomial[n, i], {i, 0, n}];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Apr 11 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 21 2019
STATUS
approved