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A275289
Number of set partitions of [n] with symmetric block size list of length three.
2
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 22 2016
STATUS
approved