%I
%S 1,1,39,2272,284319,56455146,16786728000,6935657012558,
%T 3810209706509775,2684955985258788274,2361563245536690165774,
%U 2535933313556764621139740,3265213763332455703665035736,4965602758384602312429712415116,8805913731971382862369182854094726
%N Number of colored compositions of 2n using all colors of an nset such that all parts have different color patterns and the patterns for parts i have i colors in (weakly) increasing order.
%H Vaclav Kotesovec, <a href="/A327589/b327589.txt">Table of n, a(n) for n = 0..190</a> (terms 0..120 from Alois P. Heinz)
%F a(n) = A327245(2n,n).
%F a(n) ~ c * d^n * n^(2*n), where d = 1.31520176578651896001... and c = 1.569966657460754514...  _Vaclav Kotesovec_, Sep 19 2019
%p C:= binomial:
%p b:= proc(n, i, k, p) option remember; `if`(n=0, p!, `if`(i<1, 0, add(
%p b(ni*j, min(ni*j, i1), k, p+j)*C(C(k+i1, i), j), j=0..n/i)))
%p end:
%p a:= n> add(b(2*n$2, i, 0)*(1)^(ni)*C(n, i), i=0..n):
%p seq(a(n), n=0..15);
%Y Cf. A327245.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Sep 17 2019
