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%I #5 Sep 03 2015 03:50:19
%S 1,2,3,16,21,50,205,292,587,1110,4535,5980,12447,20910,40195,142520,
%T 196291,372042,635081,1128872,1873245,6537466,8553639,16333532,
%U 26470861,46629886,73222631,127947300,385293581,518212198,939401193,1516760160,2564361235
%N 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.
%C Also matrices with two rows of nonnegative integers with distinct positive column sums and total element sum n.
%H Alois P. Heinz, <a href="/A261840/b261840.txt">Table of n, a(n) for n = 0..5000</a>
%p b:= proc(n, i, p) option remember;
%p `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p)+
%p `if`(i>n, 0, b(n-i, i-1, p+1)*(i+1))))
%p end:
%p a:= n-> b(n$2, 0):
%p seq(a(n), n=0..40);
%Y Column k=2 of A261835.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Sep 03 2015