A348703 a(n) = Sum_{x_1+x_2+ ... +x_n=n, 0 <= x_1, x_2, ... , x_n <= n} ((n-1)*n)!/((n-x_1)! * (n-x_2)! * ... * (n-x_n)!).

1, 1, 4, 510, 6745200, 19038823123320, 19549762329157865925120, 11131011767163918530071193512089600, 4977434038774545402380656971924547417738384800000

Offset: 0

Author

Seiichi Manyama, Oct 30 2021

Keywords

• nonn

Crossrefs

Cf. A000079, A092472, A348700.

Cf. A000312, A348704.

Programs

Ruby

def f(n)
  return 1 if n < 2
  (1..n).inject(:*)
end
def A(k, n)
  sum = 0
  m = f((k - 1) * n)
  (0..n).to_a.repeated_permutation(k){|i|
    if (0..k - 1).inject(0){|s, j| s + i[j]} == n
      sum += m / (0..k - 1).inject(1){|s, j| s * f(n - i[j])}
    end
  }
  sum
end
def A348703(n)
  (0..n).map{|i| A(i, i)}
end
p A348703(7)