A261774 Number of compositions of n where the (possibly scattered) maximal subsequence of part i with multiplicity j is marked with a word of length i*j over an n-ary alphabet whose letters appear in alphabetical order and all n letters occur exactly once in the composition.

1, 1, 2, 8, 29, 117, 696, 4286, 25458, 156843, 1156246, 9521096, 79140828, 665427791, 5610420458, 49509430318, 475540600965, 4831978977077, 51175720976994, 552595605354707, 5923618798039611, 63654533191518745, 705094561770919436, 8127236135685948103

Offset: 0

Author

Alois P. Heinz, Aug 31 2015

Keywords

• nonn

Examples

			a(3) = 8: 3abc, 2ab1c, 2ac1b, 2bc1a, 1a2bc, 1b2ac, 1c2ab, 1a1b1c.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A000670 (parts are marked individually), A178682 (same for partitions), A261777, A327677.

Programs

Maple

b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0,
      add(b(n-i*j, i-1, p+j)/j!*binomial(n, i*j), j=0..n/i)))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..25);

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[n == 0, p!, If[i < 1, 0, Sum[b[n - i*j, i - 1, p + j]/j!*Binomial[n, i*j], {j, 0, n/i}]]];
a[n_] := b[n, n, 0];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 17 2018, translated from Maple *)