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 A327589 Number of colored compositions of 2n using all colors of an n-set such that all parts have different color patterns and the patterns for parts i have i colors in (weakly) increasing order. 2

%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 n-set 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(n-i*j, min(n-i*j, i-1), k, p+j)*C(C(k+i-1, i), j), j=0..n/i)))

%p end:

%p a:= n-> add(b(2*n\$2, i, 0)*(-1)^(n-i)*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

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Last modified December 1 01:37 EST 2021. Contains 349426 sequences. (Running on oeis4.)