A261860 Number of compositions of n into distinct parts where each part i is marked with a word of length i over a nonary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.

12607, 1850013, 13188465, 141059073, 1056825045, 9244127655, 358616974839, 1185100976313, 6776480736882, 31512728488918, 161603593094034, 844675656403032, 26805281002135578, 67485379090772970, 310715577607315770, 1129828504295753862, 4665897718158585321

Offset

9,1

Comments

Also number of matrices with nine rows of nonnegative integer entries and without zero rows or columns such that the sum of all entries is equal to n and the column sums are distinct.

Links

Alois P. Heinz, Table of n, a(n) for n = 9..2000

Formula

a(n) = A261836(n,9).

Maple

b:= proc(n, i, p, k) option remember;
      `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p, k)+
      `if`(i>n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
    end:
a:= n->(k->add(b(n$2, 0, k-i)*(-1)^i*binomial(k, i), i=0..k))(9):
seq(a(n), n=9..30);

Crossrefs

Column k=9 of A261836.

Sequence in context: A246231 A248709 A352586 * A187136 A185841 A219332

Adjacent sequences: A261857 A261858 A261859 * A261861 A261862 A261863

Keyword

nonn

Author

Alois P. Heinz, Sep 03 2015

Status

approved