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

%I A271762 #10 May 15 2018 06:41:17
%S A271762 1,0,3,0,55,105,945,1218,15456,26785,705573,2502786,32988670,
%T A271762 169561483,1757881723,10231748010,84389906941,540218433147,
%U A271762 6899156019034,41756989590256,554960234199955,4793361957432730,59690079139252499,558283841454550850,7093218105977514525
%N A271762 Number of set partitions of [n] with minimal block length multiplicity equal to two.
%H A271762 Alois P. Heinz, <a href="/A271762/b271762.txt">Table of n, a(n) for n = 2..576</a>
%H A271762 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A271762 a(n) = A271424(n,2).
%e A271762 a(4) = 3: 12|34, 13|24, 14|23.
%p A271762 with(combinat):
%p A271762 b:= proc(n, i, k) option remember; `if`(n=0, 1,
%p A271762       `if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
%p A271762         *b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
%p A271762     end:
%p A271762 a:= n-> b(n$2, 2)-b(n$2, 3):
%p A271762 seq(a(n), n=2..30);
%t A271762 multinomial[n_, k_List] := n!/Times @@ (k!);
%t A271762 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 A271762 a[n_] := b[n, n, 2] - b[n, n, 3];
%t A271762 Table[a[n], {n, 2, 30}] (* _Jean-François Alcover_, May 15 2018, after _Alois P. Heinz_ *)
%Y A271762 Column k=2 of A271424.
%K A271762 nonn
%O A271762 2,3
%A A271762 _Alois P. Heinz_, Apr 13 2016