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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)!).

%I A348704 #13 Nov 02 2021 07:52:53
%S A348704 1,1,3,170,1027950,1079901406584,448687115051986530720,
%T A348704 89290138377185872821028908288000,
%U A348704 14759276773881730859717740767606565269685350000,2387650794422480788739162652666454048976136433287918499830000000
%N 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)!).
%H A348704 Seiichi Manyama, <a href="/A348704/b348704.txt">Table of n, a(n) for n = 0..15</a>
%o A348704 (Ruby)
%o A348704 def f(n)
%o A348704   return 1 if n < 2
%o A348704   (1..n).inject(:*)
%o A348704 end
%o A348704 def A(k, n)
%o A348704   sum = 0
%o A348704   m = f((k - 1) * n)
%o A348704   (0..n).to_a.repeated_combination(k){|i|
%o A348704     if (0..k - 1).inject(0){|s, j| s + i[j]} == n
%o A348704       sum += m / (0..k - 1).inject(1){|s, j| s * f(n - i[j])}
%o A348704     end
%o A348704   }
%o A348704   sum
%o A348704 end
%o A348704 def A348704(n)
%o A348704   (0..n).map{|i| A(i, i)}
%o A348704 end
%o A348704 p A348704(7)
%Y A348704 Cf. A027306, A092473, A348701.
%Y A348704 Cf. A005651, A348703.
%K A348704 nonn
%O A348704 0,3
%A A348704 _Seiichi Manyama_, Oct 30 2021