A261853 Number of compositions of n into distinct parts where each part i is marked with a word of length i over a binary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.

1, 10, 15, 40, 183, 266, 549, 1056, 4421, 5850, 12245, 20644, 39809, 141818, 195421, 370808, 633379, 1126518, 1870135, 6531964, 8547045, 16324018, 26458275, 46612364, 73200021, 127916094, 385244951, 518151276, 939317459, 1516648678, 2564211485, 4008404972

Offset: 2

Author

Alois P. Heinz, Sep 03 2015

Keywords

• nonn

Comments

Also number of matrices with two 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 = 2..2500

Crossrefs

Column k=2 of A261836.

Programs

Maple

b:= proc(n, i, p, k) option remember;
      `if`(i*(i+1)/2n, 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))(2):
seq(a(n), n=2..40);

Formula

a(n) = A261836(n,2).