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A181991
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n-alternating permutations of length 4n.
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4
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1, 1385, 315523, 60376809, 11593285251, 2301250545971, 472105349529479, 99537885358650089, 21451428576293883859, 4705284467293276073635, 1047067375984978044542143, 235809039854522043890582835, 53644722291938408687646120103, 12309355014854205055828909176039
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = (4*n)!*(-1/(4*n)! + 2/(n!*(3*n)!) + 1/(2*n)!^2 - 3/(n!^2*(2*n)!) + 1/n!^4). - Peter Luschny, Aug 13 2015
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MAPLE
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A181991 := proc(n) local E, dim, i, k; dim := 4*n;
E := array(0..dim, 0..dim); E[0, 0] := 1;
for i from 1 to dim do
if i mod n = 0 then E[i, 0] := 0 ;
for k from i-1 by -1 to 0 do E[k, i-k] := E[k+1, i-k-1] + E[k, i-k-1] od;
else E[0, i] := 0;
for k from 1 by 1 to i do E[k, i-k] := E[k-1, i-k+1] + E[k-1, i-k] od;
fi od; E[0, dim] end:
# Alternatively:
a := (x) -> (4*x)!*(-1/(4*x)!+2/x!/(3*x)!+1/(2*x)!^2-3/x!^2/(2*x)!+1/x!^4):
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MATHEMATICA
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A181985[n_, len_] := Module[{e, dim = n*(len - 1)}, e[0, 0] = 1; For[i = 1, i <= dim, i++, If[Mod[i, n] == 0, e[i, 0] = 0; For[k = i - 1, k >= 0, k--, e[k, i - k] = e[k + 1, i - k - 1] + e[k, i - k - 1]], e[0, i] = 0; For[k = 1, k <= i, k++, e[k, i - k] = e[k - 1, i - k + 1] + e[k - 1, i - k]]]]; Table[e[0, n*k], {k, 0, len - 1}]]; a[n_] := A181985[n, 4 + 1][[4 + 1]]; Table[a[n], {n, 1, 14}] (* Jean-François Alcover, Dec 17 2013, after Maple code in A181985 *)
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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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