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A318796 Number of 2n-length words w over an n-ary alphabet {a1, a2, ..., an} such that #(w,a1) >= #(w,a2) >= ... >= #(w,an) >= 1, where #(w,x) counts the letters x in word w.

%I A318796 #10 May 05 2022 07:13:51
%S A318796 1,1,10,180,6496,322560,25098480,2437475040,322951749120,
%T A318796 51882551360640,10494386800934400,2503138912988313600,
%U A318796 720738068391525381120,239324670990042333696000,92995858936970165240064000,41062460981196018797072640000,20742554869763399771711348736000
%N A318796 Number of 2n-length words w over an n-ary alphabet {a1, a2, ..., an} such that #(w,a1) >= #(w,a2) >= ... >= #(w,an) >= 1, where #(w,x) counts the letters x in word w.
%H A318796 Alois P. Heinz, <a href="/A318796/b318796.txt">Table of n, a(n) for n = 0..238</a>
%F A318796 a(n) = A226874(2n,n).
%e A318796 a(2) = 10: aaab, aaba, aabb, abaa, abab, abba, baaa, baab, baba, bbaa.
%p A318796 b:= proc(n, i, t) option remember;
%p A318796       `if`(t=1, 1/n!, add(b(n-j, j, t-1)/j!, j=i..n/t))
%p A318796     end:
%p A318796 a:= n-> `if`(n=0, 1, (2*n)!*b(2*n, 1, n)):
%p A318796 seq(a(n), n=0..20);
%t A318796 b[n_, i_, t_] := b[n, i, t] =
%t A318796      If[t == 1, 1/n!, Sum[b[n-j, j, t-1]/j!, {j, i, n/t}]];
%t A318796 a[n_] := If[n == 0, 1, (2n)! b[2n, 1, n]];
%t A318796 Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, May 05 2022, after _Alois P. Heinz_ *)
%Y A318796 Cf. A226874.
%K A318796 nonn
%O A318796 0,3
%A A318796 _Alois P. Heinz_, Sep 03 2018