A261861 Number of compositions of n into distinct parts where each part i is marked with a word of length i over a denary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.

333051, 4822430, 79871395, 832560780, 9644631215, 503145835150, 1977105518235, 13353202808060, 72444344358890, 431802346970780, 2638310862477610, 102808411342614000, 286995037461236030, 1470656290936993540, 5931973064021096010, 27203387338778029760

Offset

10,1

Comments

Also number of matrices with ten 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 = 10..2000

Formula

a(n) = A261836(n,10).

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))(10):
seq(a(n), n=10..30);

Crossrefs

Column k=10 of A261836.

Sequence in context: A069337 A187138 A185843 * A234129 A232412 A346028

Adjacent sequences: A261858 A261859 A261860 * A261862 A261863 A261864

Keyword

nonn

Author

Alois P. Heinz, Sep 03 2015

Status

approved