%I #12 Jun 01 2018 04:04:35
%S 1,13,171,2306,31795,446349,6357295,91615780,1333116522,19555739050,
%T 288834920011,4291094756898,64074785496631,961011037139573,
%U 14469795095794935,218624167641077960,3313409217150899536,50356639055387740752,767231549954564821746
%N Number of set partitions of [2n] with symmetric block size list of length four.
%H Alois P. Heinz, <a href="/A275293/b275293.txt">Table of n, a(n) for n = 2..834</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F a(n) ~ 2^(4*n-3) / (3*Pi*n). - _Vaclav Kotesovec_, Aug 02 2016
%e a(3) = 13: 12|3|4|56, 13|2|4|56, 1|23|45|6, 1|23|46|5, 14|2|3|56, 1|24|35|6, 1|24|36|5, 1|25|34|6, 1|26|34|5, 15|2|3|46, 1|25|36|4, 1|26|35|4, 16|2|3|45.
%p a:= proc(n) option remember; `if`(n<3, [0$2, 1, 13][n+1],
%p ((n-1)*(4320-23328*n+1365*n^6-11072*n^5+35733*n^4
%p -58702*n^3+51744*n^2)*a(n-1)-(4*(2*n-5))*(n-1)*(n-2)
%p *(2*n-3)*(21*n^3-55*n^2+44*n-12)*a(n-2))/((2*(n-2))*
%p (2*n-1)*(21*n^3-118*n^2+217*n-132)*n^2))
%p end:
%p seq(a(n), n=2..30);
%t a[2] = 1; a[3] = 13; a[n_] := a[n] = ((n-1)*(4320 - 23328*n + 1365*n^6 - 11072*n^5 + 35733*n^4 - 58702*n^3 + 51744*n^2)*a[n-1] - (4*(2*n-5))*(n-1) *(n-2)*(2*n-3)*(21*n^3 - 55*n^2 + 44*n - 12)*a[n-2])/((2*(n-2))*(2*n-1)* (21*n^3 - 118*n^2 + 217*n - 132)*n^2);
%t Table[a[n], {n, 2, 30}] (* _Jean-François Alcover_, Jun 01 2018, from Maple *)
%Y Bisection of column k=4 of A275281.
%K nonn
%O 2,2
%A _Alois P. Heinz_, Jul 22 2016
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