|
%I #11 Dec 14 2020 08:32:08
%S 1,1,41,8020,4396189,5226876501,11581358373398,43225961160925257,
%T 252807246693691825421,2194141947654736889023357,
%U 27084992620572948369385642201,459597167193175440533390098112664,10424556988338412210154331381461375830
%N Number of colored set partitions of [2n] where colors of the elements of subsets are distinct and in increasing order and exactly n colors are used.
%H Alois P. Heinz, <a href="/A325481/b325481.txt">Table of n, a(n) for n = 0..151</a>
%F a(n) = A322670(2n,n).
%p b:= proc(n, k) option remember; `if`(n=0, 1, add(b(n-j, k)*
%p binomial(n-1, j-1)*binomial(k, j), j=1..min(k, n)))
%p end:
%p a:= n-> add(b(2*n, n-i)*(-1)^i*binomial(n, i), i=0..n):
%p seq(a(n), n=0..14);
%t b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - j, k] Binomial[n - 1, j - 1] Binomial[k, j], {j, 1, Min[k, n]}]];
%t a[n_] := Sum[b[2n, n - i] (-1)^i Binomial[n, i], {i, 0, n}];
%t a /@ Range[0, 14] (* _Jean-François Alcover_, Dec 14 2020, after _Alois P. Heinz_ *)
%Y Cf. A322670.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Sep 06 2019
|
