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A328156
Number of set partitions of [2n] with distinct block sizes and one of the block sizes is n.
4
1, 0, 0, 60, 280, 3780, 74844, 576576, 6949800, 110416020, 3319141540, 31333878576, 545777101324, 8349081650000, 196469122903200, 8108831645948160, 99934219113287400, 1961077012271694900, 39215221761564594900, 860948656518718429200, 25274389422461123124180
OFFSET
0,4
LINKS
FORMULA
a(n) = A327869(2n,n).
MAPLE
b:= proc(n, i, k) option remember; `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!)))
end:
a:= n-> (2*n)!*(b(2*n$2, 0)-`if`(n=0, 0, b(2*n$2, n))):
seq(a(n), n=0..22);
MATHEMATICA
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!]]];
a[n_] := (2n)! (b[2n, 2n, 0] - If[n == 0, 0, b[2n, 2n, n]]);
a /@ Range[0, 22] (* Jean-François Alcover, May 02 2020, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 05 2019
STATUS
approved