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

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Wikipedia, Partition of a set

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

Crossrefs

Column k=3 of A275281.

Sequence in context: A030224 A114624 A091024 * A151430 A083309 A318264

Adjacent sequences: A275286 A275287 A275288 * A275290 A275291 A275292

Keyword

nonn

Author

Alois P. Heinz, Jul 22 2016

Status

approved