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A250286
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Number of permutations p of [n] such that p(i) > p(i+1) iff i == 0 (mod 9).
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3
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 54, 219, 714, 2001, 5004, 11439, 24309, 48619, 831384, 9069651, 64369341, 355150566, 1635163542, 6542615421, 23369110326, 75953123676, 227864057851, 5742168041637, 90830731860000, 920922875075934, 7159714782188364
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OFFSET
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0,11
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LINKS
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MAPLE
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b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
`if`(t=0, add(b(u-j, o+j-1, irem(t+1, 9)), j=1..u),
add(b(u+j-1, o-j, irem(t+1, 9)), j=1..o)))
end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..35);
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MATHEMATICA
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nmax = 30; CoefficientList[Series[1 + Sum[(x^(9 - k) * HypergeometricPFQ[{1}, {10/9 - k/9, 11/9 - k/9, 4/3 - k/9, 13/9 - k/9, 14/9 - k/9, 5/3 - k/9, 16/9 - k/9, 17/9 - k/9, 2 - k/9}, -x^9/387420489])/(9 - k)!, {k, 0, 8}] / HypergeometricPFQ[{}, {1/9, 2/9, 1/3, 4/9, 5/9, 2/3, 7/9, 8/9}, -x^9/387420489], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Apr 21 2021 *)
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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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