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A262164
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Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 2.
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3
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1, 1, 2, 4, 16, 54, 324, 1532, 12256, 74512, 745120, 5536752, 66441024, 583466480, 8168530720, 82769713504, 1324315416064, 15208157533440, 273746835601920, 3513491887566848, 70269837751336960, 996837786288583168, 21930431298348829696, 340730692136161864704
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OFFSET
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0,3
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LINKS
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FORMULA
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MAPLE
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b:= proc(u, o, c) option remember; `if`(c<0 or c>2, 0, `if`(u+o=0,
x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..2))(add(
b(u-j, o-1+j, c-1), j=1..u)+add(b(u+j-1, o-j, c+1), j=1..o))))
end:
a:= n-> (p-> add(coeff(p, x, i), i=0..min(n, 2)))(b(0, n, 0)):
seq(a(n), n=0..25);
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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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