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%I #9 Sep 24 2019 20:26:38
%S 0,0,3,18,60,210,798,2462,7891,25148,84173,257558,810924,2515962,
%T 7706020,24261554,73746402,224417982,683672754,2057559942,6177146990,
%U 18671429714,55589344618,165403412230,491940143015,1452537550800,4280665171599,12578264746522
%N Number of colored compositions of n using all colors of a 2-set such that all parts have different color patterns and the patterns for parts i are sorted and have i colors (in arbitrary order).
%H Alois P. Heinz, <a href="/A327768/b327768.txt">Table of n, a(n) for n = 0..800</a>
%e a(2) = 3: 2ab, 2ba, 1a1b.
%e a(3) = 18: 3aab, 3aba, 3baa, 3abb, 3bab, 3bba, 2aa1b, 2ab1a, 2ba1a, 2ab1b, 2ba1b, 2bb1a, 1a2ab, 1a2ba, 1a2bb, 1b2aa, 1b2ab, 1b2ba.
%p b:= proc(n, i, k, p) option remember;
%p `if`(n=0, p!, `if`(i<1, 0, add(binomial(k^i, j)*
%p b(n-i*j, min(n-i*j, i-1), k, p+j)/j!, j=0..n/i)))
%p end:
%p a:= n-> (k-> add(b(n$2, i, 0)*(-1)^(k-i)*binomial(k, i), i=0..k))(2):
%p seq(a(n), n=0..27);
%Y Column k=2 of A327673.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Sep 24 2019
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