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A097592
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Triangle read by rows: T(n,k) is the number of permutations of [n] with k increasing runs of even length.
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0
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1, 1, 1, 1, 2, 4, 7, 12, 5, 25, 52, 43, 102, 299, 258, 61, 531, 1750, 1853, 906, 3141, 11195, 15634, 8965, 1385, 20218, 83074, 133697, 94398, 31493, 146215, 675304, 1207256, 1088575, 460929, 50521, 1174889, 5880354, 11974457, 12625694, 6632158
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row n has 1+floor(n/2) entries.
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FORMULA
| E.g.f.=2(t-1)u/[ -2u+(2-t+tu)exp((-1+u)x/2)+(t-2+tu)exp(-(1+u)x/2)], where u=sqrt(5-4t).
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EXAMPLE
| Triangle starts:
1;
1;
1,1;
2,4;
7,12,5;
25,52,43;
102,299,258,61;
Example: T(4,2)=5 because we have 13/24, 14/23, 23/14, 24/13 and 34/12.
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MAPLE
| G:=2*(t-1)*u/(-2*u+(2-t+t*u)*exp((-1+u)*x/2)+(t-2+t*u)*exp(-(1+u)*x/2)): u:=sqrt(5-4*t): Gser:=simplify(series(G, x=0, 12)): P[0]:=1: for n from 1 to 11 do P[n]:=sort(n!*coeff(Gser, x^n)) od: seq(seq(coeff(t*P[n], t^k), k=1..1+floor(n/2)), n=0..11);
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CROSSREFS
| Sequence in context: A084992 A153555 A058103 * A193841 A052474 A033054
Adjacent sequences: A097589 A097590 A097591 * A097593 A097594 A097595
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KEYWORD
| nonn,tabf
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 29 2004
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