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A275282 Number of set partitions of [n] with symmetric block size list.

%I A275282 #10 May 27 2018 11:01:53
%S A275282 1,1,2,2,7,9,47,80,492,985,7197,16430,139316,361737,3425683,9939134,
%T A275282 103484333,329541459,3747921857,12980700318,159811532315,598410986533,
%U A275282 7902918548186,31781977111506,447462660895105,1920559118957107,28699615818386524,130838216971937408
%N A275282 Number of set partitions of [n] with symmetric block size list.
%H A275282 Alois P. Heinz, <a href="/A275282/b275282.txt">Table of n, a(n) for n = 0..400</a>
%H A275282 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A275282 a(n) = Sum_{k=0..n} A275281(n,k).
%e A275282 a(3) = 2: 123, 1|2|3.
%e A275282 a(4) = 7: 1234, 12|34, 13|24, 14|23, 1|23|4, 1|24|3, 1|2|3|4.
%e A275282 a(5) = 9: 12345, 12|3|45, 13|2|45, 1|234|5, 1|235|4, 14|2|35, 1|245|3, 15|2|34, 1|2|3|4|5.
%p A275282 b:= proc(n, s) option remember; `if`(n>s,
%p A275282       binomial(n-1, n-s-1), 1) +add(binomial(n-1, j-1)*
%p A275282       b(n-j, s+j) *binomial(s+j-1, j-1), j=1..(n-s)/2)
%p A275282     end:
%p A275282 a:= n-> b(n, 0):
%p A275282 seq(a(n), n=0..30);
%t A275282 b[n_, s_] := b[n, s] = If[n > s, Binomial[n-1, n-s-1], 1] + Sum[Binomial[n - 1, j - 1]*b[n - j, s + j]*Binomial[s + j - 1, j - 1], {j, 1, (n-s)/2}];
%t A275282 a[n_] := b[n, 0];
%t A275282 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 27 2018, from Maple *)
%Y A275282 Row sums of A275281.
%K A275282 nonn
%O A275282 0,3
%A A275282 _Alois P. Heinz_, Jul 21 2016