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A072949
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Number of permutations p of {1,2,3,...,n} such that Sum_{k=1..n} abs(k-p(k)) = 2n.
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3
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1, 0, 0, 0, 4, 24, 148, 744, 3696, 17640, 83420, 390144, 1817652, 8438664, 39117852, 181136304, 838372452, 3879505944, 17952463180, 83086702848, 384626048292, 1781018204328, 8249656925564, 38225193868560, 177179811427796, 821544012667704, 3810648054607212
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OFFSET
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0,5
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COMMENTS
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LINKS
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MAPLE
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with(linalg): f := (i, j) -> x^(abs(i-j)):for n from 1 to 17 do A := matrix(n, n, f): printf("%d, ", coeff(permanent(A), x, 2*n)) od: # Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 27 2008
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MATHEMATICA
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g[h_, n_] := g[h, n] = Module[{i, j}, {i, j} = QuotientRemainder[h, 2]; 1 - If[h==n, 0, (i+1)*z*t^(i+j)/g[h+1, n]]]; a[n_ /; n<4] = 0; a[n_] := SeriesCoefficient[1/g[0, n], {z, 0, n}, {t, 0, n}]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 26}] (* Jean-François Alcover, Jan 07 2016, after Alois P. Heinz *)
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PROG
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(PARI) a(n)=sum(k=1, n!, if(sum(i=1, n, abs(i-component(numtoperm(n, k), i)))-2*n, 0, 1))
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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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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 27 2008
a(22)-a(26) from Alois P. Heinz, May 02 2014 using formula given by Guay-Paquey and Petersen
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STATUS
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approved
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