A348704 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, 3, 170, 1027950, 1079901406584, 448687115051986530720, 89290138377185872821028908288000, 14759276773881730859717740767606565269685350000, 2387650794422480788739162652666454048976136433287918499830000000

Offset: 0

Author

Seiichi Manyama, Oct 30 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..15

Crossrefs

Cf. A027306, A092473, A348701.

Cf. A005651, A348703.

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_combination(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 A348704(n)
  (0..n).map{|i| A(i, i)}
end
p A348704(7)