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Search: id:A134432
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| A134432 |
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Sum of entries in all the arrangements of the set {1,2,...,n} (to n=0 there corresponds the empty set). |
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+0
2
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| 0, 1, 9, 66, 490, 3915, 34251, 328804, 3452436, 39456405, 488273005, 6510306726, 93097386174, 1421850988831, 23105078568495, 398118276872520, 7251440043035176, 139227648826275369
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OFFSET
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0,3
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COMMENT
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a(n)=Sum(k*A134431(n,k),k=0..n(n+1)/2).
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FORMULA
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a(n)=diff(P[n](t), t) evaluated at t=1; here P[n](t)=Q[n](t,1) where the polynomials Q[n](t,x) are defined by Q[0]=1 and Q[n]=Q[n-1] + xt^n diff(xQ[n-1], x). [Q[n](t,x) is the bivariate generating polynomial of the arrangements of {1,2,...,n}, where t (x) marks the sum (number) of the entries; for example, Q[2](t,x)=1+tx + t^2*x + 2t^3*x^2, corresponding to: empty, 1, 2, 12, and 21, respectively.]
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EXAMPLE
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a(2)=9 because the arrangements of {1,2} are: empty, 1, 2, 12, and 21.
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MAPLE
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Q[0]:=1: for n to 17 do Q[n]:=sort(simplify(Q[n-1]+t^n*x*(diff(x*Q[n-1], x))), t) end do: for n from 0 to 17 do P[n]:=sort(subs(x=1, Q[n])) end do: seq(subs(t =1, diff(P[n], t)), n=0..17);
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CROSSREFS
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Cf. A000522, A134431.
Sequence in context: A055148 A014830 A048439 this_sequence A098107 A091647 A106132
Adjacent sequences: A134429 A134430 A134431 this_sequence A134433 A134434 A134435
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 16 2007
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