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%I #12 May 02 2020 04:49:27
%S 1,0,0,60,280,3780,74844,576576,6949800,110416020,3319141540,
%T 31333878576,545777101324,8349081650000,196469122903200,
%U 8108831645948160,99934219113287400,1961077012271694900,39215221761564594900,860948656518718429200,25274389422461123124180
%N Number of set partitions of [2n] with distinct block sizes and one of the block sizes is n.
%H Alois P. Heinz, <a href="/A328156/b328156.txt">Table of n, a(n) for n = 0..510</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F a(n) = A327869(2n,n).
%p b:= proc(n, i, k) option remember; `if`(i*(i+1)/2<n, 0,
%p `if`(n=0, 1, `if`(i<2, 0, b(n, i-1, `if`(i=k, 0, k)))+
%p `if`(i=k, 0, b(n-i, min(n-i, i-1), k)/i!)))
%p end:
%p a:= n-> (2*n)!*(b(2*n$2, 0)-`if`(n=0, 0, b(2*n$2, n))):
%p seq(a(n), n=0..22);
%t b[n_, i_, k_] := b[n, i, k] = If[i (i + 1)/2 < n, 0, If[n == 0, 1, If[i < 2, 0, b[n, i - 1, If[i == k, 0, k]]] + If[i == k, 0, b[n - i, Min[n - i, i - 1], k]/i!]]];
%t a[n_] := (2n)! (b[2n, 2n, 0] - If[n == 0, 0, b[2n, 2n, n]]);
%t a /@ Range[0, 22] (* _Jean-François Alcover_, May 02 2020, after Maple *)
%Y Cf. A266518, A276961, A327869.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Oct 05 2019
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