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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. 4
1, 1, 2, 8, 29, 117, 696, 4286, 25458, 156843, 1156246, 9521096, 79140828, 665427791, 5610420458, 49509430318, 475540600965, 4831978977077, 51175720976994, 552595605354707, 5923618798039611, 63654533191518745, 705094561770919436, 8127236135685948103 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, May 17 2018, translated from Maple *)

CROSSREFS

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

Sequence in context: A302266 A011367 A220547 * A345131 A150733 A150734

Adjacent sequences:  A261771 A261772 A261773 * A261775 A261776 A261777

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 31 2015

STATUS

approved

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Last modified July 25 23:39 EDT 2021. Contains 346294 sequences. (Running on oeis4.)