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A307005
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Expansion of e.g.f. (2*exp(x)-2*x-x^2)/(2-2*x-x^2).
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2
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1, 1, 3, 13, 71, 486, 3982, 38081, 416145, 5116222, 69888746, 1050168417, 17214678241, 305703953660, 5846391071172, 119794781201881, 2618283427770737, 60802908515558346, 1495049717728972990, 38803241993010963977, 1060124286228724147641, 30411290829335509535632
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OFFSET
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0,3
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COMMENTS
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Number of totally ordered partitions on an n-element set where each non-minimal class contains at most 2 elements.
Convention a(0) = 1.
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LINKS
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FORMULA
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Recurrence: a(1) = 1, a(2) = 3, a(n+2) = 1 + (n+2)*a(n+1) + (1/2)*(n+2)*(n+1)*a(n).
a(n) = Sum_{i=0..n} (n!/(n + 1 - i)!)*((sqrt(3)/3)*((1 + sqrt(3))/2)^i - (sqrt(3)/3)*((1 - sqrt(3))/2)^i).
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MATHEMATICA
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Nest[Append[#1, 1 + #2 #1[[-1]] + #2 (#2 - 1) #1[[-2]]/2 ] & @@ {#, Length@ #} &, {1, 1, 3}, 19] (* Michael De Vlieger, Apr 21 2019 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec(serlaplace((2*exp(x)-2*x-x^2)/(2-2*x-x^2))) \\ Felix Fröhlich, Mar 19 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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