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A152877
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Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} having k consecutive triples of the form (odd,even,odd) and (even,odd,even) (0<=k<=n-2).
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5
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1, 1, 2, 4, 2, 16, 0, 8, 60, 24, 24, 12, 288, 144, 216, 0, 72, 1584, 1296, 1152, 576, 288, 144, 10368, 9216, 10368, 4608, 4608, 0, 1152, 74880, 83520, 86400, 60480, 31680, 17280, 5760, 2880, 604800, 748800, 892800, 576000, 460800, 172800, 144000, 0, 28800
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OFFSET
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0,3
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COMMENTS
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Row n has n-1 entries (n>=2).
Sum of entries in row n is n! (A000142(n)).
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LINKS
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FORMULA
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It would be good to have a formula or generating function for this sequence (a formula for column 0 is given in A152876).
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EXAMPLE
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T(3,1) = 2 because we have 123 and 321.
Triangle starts:
1;
1;
2;
4, 2;
16, 0, 8;
60, 24, 24, 12;
288, 144, 216, 0, 72;
1584, 1296, 1152, 576, 288, 144;
10368, 9216, 10368, 4608, 4608, 0, 1152;
...
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MAPLE
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b:= proc(o, u, t) option remember; `if`(u+o=0, 1, expand(
o*b(o-1, u, [2, 2, 5, 5, 2][t])*`if`(t=4, x, 1)+
u*b(o, u-1, [3, 4, 3, 3, 4][t])*`if`(t=5, x, 1)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(
b(ceil(n/2), floor(n/2), 1)):
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MATHEMATICA
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b[o_, u_, t_] := b[o, u, t] = If[u+o == 0, 1, Expand[o*b[o-1, u, {2, 2, 5, 5, 2}[[t]]]*If[t == 4, x, 1] + u*b[o, u-1, {3, 4, 3, 3, 4}[[t]]]*If[t == 5, x, 1]]]; T[n_] := Function[{p}, Table[Coefficient[p, x, i], {i, 0, Exponent[p, x]}]] [b[Ceiling[n/2], Floor[n/2], 1]]; Table[T[n], {n, 0, 12}] // Flatten (* Jean-François Alcover, May 27 2015, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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