A261777 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 n-ary alphabet whose letters appear in alphabetical order and all n letters occur exactly once in the composition.

1, 1, 3, 19, 115, 951, 10281, 116313, 1436499, 20203795, 338834053, 5824666893, 108142092169, 2118605140237, 44375797806315, 1039641056342619, 25413053107195539, 646983321301050147, 17311013062443870681, 481282277347815404745, 13913039361920333694165

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

Example

a(3) = 19: 3a|b|c, 3a|c|b, 3b|a|c, 3b|c|a, 3c|a|b, 3c|b|a, 2a|b1c, 2b|a1c, 2a|c1b, 2c|a1b, 2b|c1a, 2c|b1a, 1a2b|c, 1a2c|b, 1b2a|c, 1b2c|a, 1c2a|b, 1c2b|a, 111abc.

Maple

with(combinat):
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!*multinomial(n, n-i*j, j$i), j=0..n/i)))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..25);

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
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!*multinomial[n, Join[{n - i*j}, Table[j, {i}]]], {j, 0, n/i}]]];
a[n_] := b[n, n, 0];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Mar 04 2022, after Alois P. Heinz *)

Crossrefs

Cf. A000670, A261774.

Sequence in context: A267802 A229928 A309183 * A037781 A037585 A084133

Adjacent sequences: A261774 A261775 A261776 * A261778 A261779 A261780

Keyword

nonn

Author

Alois P. Heinz, Aug 31 2015

Status

approved