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A124325
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Number of blocks of size >1 in all partitions of an n-set.
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6
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0, 0, 1, 4, 17, 76, 362, 1842, 9991, 57568, 351125, 2259302, 15288000, 108478124, 805037105, 6233693772, 50257390937, 421049519856, 3659097742426, 32931956713294, 306490813820239, 2945638599347760, 29198154161188501
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OFFSET
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0,4
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COMMENTS
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Sum of the first entries in all blocks of all set partitions of [n-1]. a(4) = 17 because the sum of the first entries in all blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 1+4+3+3+6 = 17. - Alois P. Heinz, Apr 24 2017
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LINKS
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FORMULA
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a(n) = B(n+1)-B(n)-n*B(n-1), where B(q) are the Bell numbers (A000110).
E.g.f.: (exp(z)-1-z)*exp(exp(z)-1).
a(n) = Sum_{k=0..floor(n/2)} k*A124324(n,k).
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EXAMPLE
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a(3) = 4 because in the partitions 123, 12|3, 13|2, 1|23, 1|2|3 we have four blocks of size >1.
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MAPLE
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with(combinat): c:=n->bell(n+1)-bell(n)-n*bell(n-1): seq(c(n), n=0..23);
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MATHEMATICA
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nn=22; Range[0, nn]!CoefficientList[Series[(Exp[x]-1-x)Exp[Exp[x]-1], {x, 0, nn}], x] (* Geoffrey Critzer, Mar 28 2013 *)
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PROG
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(PARI)
N = 66; x = 'x + O('x^N);
egf = (exp(x)-1-x)*exp(exp(x)-1) + 'c0;
gf = serlaplace(egf);
v = Vec(gf); v[1]-='c0; v
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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