A275289 Number of set partitions of [n] with symmetric block size list of length three.

1, 2, 7, 19, 56, 160, 463, 1337, 3874, 11241, 32682, 95172, 277577, 810706, 2370839, 6941473, 20345618, 59692831, 175295996, 515217034, 1515478535, 4460940067, 13140081770, 38729776774, 114221851951, 337050020750, 995097461503, 2939337252651, 8686270661400

Offset: 3

Author

Alois P. Heinz, Jul 22 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..1000
• Wikipedia, Partition of a set

Crossrefs

Column k=3 of A275281.

Formula

G.f.: -(1/2)*(3*x-1+sqrt((1-3*x)*(x+1)*(2*x-1)^2))/((3*x-1)*(x+1)).

a(n) ~ 3^(n-1/2) / (4*sqrt(Pi*n)). - Vaclav Kotesovec, Aug 02 2016

Recurrence: (n-3)*n*a(n) = (n^2 - 3*n + 4)*a(n-1) + (n-2)*(5*n - 11)*a(n-2) + 3*(n-3)*(n-2)*a(n-3). - Vaclav Kotesovec, Aug 02 2016

From Mélika Tebni, Jun 20 2025: (Start)

a(n) = Sum_{k=floor(n/2)..n-2} binomial(n-1, k+1)*binomial(k, n-(k+1)).

Inverse binomial transform of A371965. (End)