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

0,3

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A369299 A011367 A220547 * A345131 A150733 A150734

Adjacent sequences: A261771 A261772 A261773 * A261775 A261776 A261777

Keyword

nonn

Author

Alois P. Heinz, Aug 31 2015

Status

approved