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A097591
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Triangle read by rows: T(n,k) is the number of permutations of [n] with k increasing runs of odd length.
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0
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1, 0, 1, 1, 0, 1, 0, 5, 0, 1, 6, 0, 17, 0, 1, 0, 70, 0, 49, 0, 1, 90, 0, 500, 0, 129, 0, 1, 0, 1890, 0, 2828, 0, 321, 0, 1, 2520, 0, 23100, 0, 13930, 0, 769, 0, 1, 0, 83160, 0, 215292, 0, 62634, 0, 1793, 0, 1, 113400, 0, 1549800, 0, 1697430, 0, 264072, 0, 4097, 0, 1, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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FORMULA
| E.g.f.=t^2/[1-tx-(1-t^2)exp(-tx)].
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EXAMPLE
| Triangle starts:
1;
0,1;
1,0,1;
0,5,0,1;
6,0,17,0,1;
0,70,0,49,0,1;
Row n has n+1 entries.
Example: T(3,1)=5 because we have (123),13(2),(2)13,23(1) and (3)12 (the runs of odd length are shown between parentheses).
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MAPLE
| G:=t^2/(1-t*x-(1-t^2)*exp(-t*x)): Gser:=simplify(series(G, x=0, 12)): P[0]:=1: for n from 1 to 11 do P[n]:=sort(expand(n!*coeff(Gser, x^n))) od: seq(seq(coeff(t*P[n], t^k), k=1..n+1), n=0..11);
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CROSSREFS
| Sequence in context: A060081 A197515 A083861 * A164652 A127557 A060524
Adjacent sequences: A097588 A097589 A097590 * A097592 A097593 A097594
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KEYWORD
| nonn,tabl
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 29 2004
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