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A327841 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 (weakly) increasing order.

%I A327841 #5 Sep 27 2019 19:46:46
%S A327841 0,0,2,10,27,70,223,508,1193,2822,7048,15690,35072,79018,167667,
%T A327841 382976,823599,1742082,3765187,7785290,16299074,34337380,70503188,
%U A327841 143916326,296390373,597048414,1202172962,2416614660,4813022691,9551780272,18833189269,37248671816
%N A327841 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 (weakly) increasing order.
%H A327841 Alois P. Heinz, <a href="/A327841/b327841.txt">Table of n, a(n) for n = 0..1000</a>
%p A327841 b:= proc(n, i, k, p) option remember; `if`(n=0, p!,
%p A327841       `if`(i<1, 0, add(b(n-i*j, min(n-i*j, i-1), k, p+j)/
%p A327841        j!*binomial(binomial(k+i-1, i), j), j=0..n/i)))
%p A327841     end:
%p A327841 a:= n-> (k-> add(b(n$2, i, 0)*(-1)^(k-i)*
%p A327841          binomial(k, i), i=0..k))(2):
%p A327841 seq(a(n), n=0..35);
%Y A327841 Column k=2 of A327244.
%K A327841 nonn
%O A327841 0,3
%A A327841 _Alois P. Heinz_, Sep 27 2019