A261856 Number of compositions of n into distinct parts where each part i is marked with a word of length i over a quinary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.

31, 1305, 4955, 26765, 124450, 2008546, 4399870, 17016950, 51516925, 187653115, 2298210803, 4405690315, 14002637160, 37448507530, 109070884580, 308549728478, 3711879979775, 6377942356265, 19056675979455, 45667548869495, 122550455798230, 293681447602030

Offset

5,1

Comments

Also number of matrices with five 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 = 5..2500

Formula

a(n) = A261836(n,5).

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))(5):
seq(a(n), n=5..30);

Crossrefs

Column k=5 of A261836.

Sequence in context: A182784 A139162 A078961 * A049292 A289473 A069406

Adjacent sequences: A261853 A261854 A261855 * A261857 A261858 A261859

Keyword

nonn

Author

Alois P. Heinz, Sep 03 2015

Status

approved