A275293 Number of set partitions of [2n] with symmetric block size list of length four.

1, 13, 171, 2306, 31795, 446349, 6357295, 91615780, 1333116522, 19555739050, 288834920011, 4291094756898, 64074785496631, 961011037139573, 14469795095794935, 218624167641077960, 3313409217150899536, 50356639055387740752, 767231549954564821746

Offset: 2

Author

Alois P. Heinz, Jul 22 2016

Keywords

• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..834
• Wikipedia, Partition of a set

Crossrefs

Bisection of column k=4 of A275281.

Programs

Maple

a:= proc(n) option remember; `if`(n<3, [0$2, 1, 13][n+1],
      ((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))
    end:
seq(a(n), n=2..30);

Mathematica

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);
Table[a[n], {n, 2, 30}] (* Jean-François Alcover, Jun 01 2018, from Maple *)

Formula

a(n) ~ 2^(4*n-3) / (3*Pi*n). - Vaclav Kotesovec, Aug 02 2016