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A216964
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Triangle read by rows, arising in enumeration of permutations by cyclic valleys, cycles and fixed points.
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1
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1, 2, 6, 22, 2, 94, 26, 460, 244, 16, 2532, 2124, 384, 15420, 18536, 6092, 272, 102620, 166440, 83436, 10384, 739512, 1550864, 1082712, 247776, 7936, 5729192, 15040112, 13841928, 4864480, 441088, 47429896, 151960264, 177512632, 87003032, 14741984, 353792
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OFFSET
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1,2
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COMMENTS
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See Ma and Chow (2012) for precise definition (see Corollary 5).
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LINKS
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EXAMPLE
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Triangle begins:
1
2
6
22, 2
94, 26
460, 244, 16
2532, 2124, 384
...
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MATHEMATICA
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rows = 12;
Reap[For[P = x*y; n = 1; Sow[{1}], n < rows, n++, P = (n*q + x*y)*P + 2*q*(1-q)*D[P, q] + 2*x*(1-q)*D[P, x] + (1-2*y+q*y)*D[P, y] // Simplify; Sow[CoefficientList[P /. {x -> 1, y -> 1}, q]]]][[2, 1]] // Flatten (* Jean-François Alcover, Sep 23 2018, from PARI *)
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PROG
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(PARI) tabf(m) = {P = x*y; for (n=1, m, M = subst(P, x, 1); M = subst(M, y, 1); for (d=0, poldegree(M, q), print1(polcoeff(M, d, q), ", "); ); print(""); P = (n*q+x*y)*P + 2*q*(1-q)*deriv(P, q)+ 2*x*(1-q)*deriv(P, x)+ (1-2*y+q*y)*deriv(P, y); ); } \\ Michel Marcus, Feb 08 2013
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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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