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A037256
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a(n) = n!*Sum_{i=0..n-1} (n-i)*(-2)^i/(i+1)!.
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6
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0, 1, 2, 10, 48, 296, 2080, 16752, 151424, 1519744, 16766208, 201685760, 2627316736, 36847260672, 553551644672, 8868624615424, 150943592939520, 2719816264613888, 51724646086475776, 1035359388788391936, 21759010038674358272, 479027478333199482880
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OFFSET
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0,3
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COMMENTS
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Arises from "Unfriendly Seating Arrangement" problem around a circular table.
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LINKS
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FORMULA
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E.g.f.: (1-exp(-2*x))*(1-x)^(-2)/2.
a(n) = 2*(n-1)*a(n-1) - (n-4)*(n-1)*a(n-2) - 2*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Oct 08 2012
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MAPLE
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f:=n->n!*add((n-i)*(-2)^i/(i+1)!, i=0..n-1);
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MATHEMATICA
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m = 19; CoefficientList[ Series[(1 - Exp[-2x])*(1/((1-x)^2*2)), {x, 0, m}], x]*Range[0, m]!
Flatten[{0, Table[n!*Sum[Sum[(-1)^j*2^j/(j+1)!, {j, 0, k}], {k, 0, n-1}], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 27 2012 *)
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PROG
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(PARI) x='x+O('x^66); concat([0], Vec(serlaplace((1-exp(-2*x))/(2*(1-x)^2)))) \\ Joerg Arndt, May 04 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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