%I
%S 1,1,3,19,115,951,10281,116313,1436499,20203795,338834053,5824666893,
%T 108142092169,2118605140237,44375797806315,1039641056342619,
%U 25413053107195539,646983321301050147,17311013062443870681,481282277347815404745,13913039361920333694165
%N Number of compositions of n where the (possibly scattered) maximal subsequence of part i with multiplicity j is marked with i words of length j over an nary alphabet whose letters appear in alphabetical order and all n letters occur exactly once in the composition.
%H Alois P. Heinz, <a href="/A261777/b261777.txt">Table of n, a(n) for n = 0..400</a>
%e a(3) = 19: 3abc, 3acb, 3bac, 3bca, 3cab, 3cba, 2ab1c, 2ba1c, 2ac1b, 2ca1b, 2bc1a, 2cb1a, 1a2bc, 1a2cb, 1b2ac, 1b2ca, 1c2ab, 1c2ba, 111abc.
%p with(combinat):
%p b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0, add(
%p b(ni*j, i1, p+j)/j!*multinomial(n, ni*j, j$i), j=0..n/i)))
%p end:
%p a:= n> b(n$2, 0):
%p seq(a(n), n=0..25);
%Y Cf. A000670, A261774.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 31 2015
