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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.
2
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
2,2
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
FORMULA
a(n) = A261836(n,2).
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))(2):
seq(a(n), n=2..40);
CROSSREFS
Column k=2 of A261836.
Sequence in context: A078818 A194267 A372044 * A259629 A212794 A048061
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 03 2015
STATUS
approved