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 A271762 Number of set partitions of [n] with minimal block length multiplicity equal to two. 2

%I #10 May 15 2018 06:41:17

%S 1,0,3,0,55,105,945,1218,15456,26785,705573,2502786,32988670,

%T 169561483,1757881723,10231748010,84389906941,540218433147,

%U 6899156019034,41756989590256,554960234199955,4793361957432730,59690079139252499,558283841454550850,7093218105977514525

%N Number of set partitions of [n] with minimal block length multiplicity equal to two.

%H Alois P. Heinz, <a href="/A271762/b271762.txt">Table of n, a(n) for n = 2..576</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%F a(n) = A271424(n,2).

%e a(4) = 3: 12|34, 13|24, 14|23.

%p with(combinat):

%p b:= proc(n, i, k) option remember; `if`(n=0, 1,

%p `if`(i<1, 0, add(multinomial(n, n-i*j, i\$j)

%p *b(n-i*j, i-1, k)/j!, j={0, \$k..n/i})))

%p end:

%p a:= n-> b(n\$2, 2)-b(n\$2, 3):

%p seq(a(n), n=2..30);

%t multinomial[n_, k_List] := n!/Times @@ (k!);

%t b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[multinomial[n, Join[{n - i*j}, Table[i, j]]]*b[n - i*j, i - 1, k]/j!, {j, Join[{0}, Range[k, n/i]]}]]];

%t a[n_] := b[n, n, 2] - b[n, n, 3];

%t Table[a[n], {n, 2, 30}] (* _Jean-François Alcover_, May 15 2018, after _Alois P. Heinz_ *)

%Y Column k=2 of A271424.

%K nonn

%O 2,3

%A _Alois P. Heinz_, Apr 13 2016

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Last modified August 12 12:46 EDT 2024. Contains 375092 sequences. (Running on oeis4.)