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A322295
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Number of permutations of [2n] with exactly n rising or falling successions.
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3
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1, 2, 10, 120, 2198, 54304, 1674468, 61736880, 2644978110, 129019925424, 7056278570108, 427516982398576, 28417031969575260, 2055803302988520320, 160786792285272198088, 13517797622576903566560, 1215656330296317906395790, 116440107306323155369822800
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OFFSET
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0,2
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LINKS
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FORMULA
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MAPLE
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S:= proc(n) option remember; `if`(n<4, [1, 1, 2*t, 4*t+2*t^2]
[n+1], expand((n+1-t)*S(n-1) -(1-t)*(n-2+3*t)*S(n-2)
-(1-t)^2*(n-5+t)*S(n-3) +(1-t)^3*(n-3)*S(n-4)))
end:
a:= n-> coeff(S(2*n), t, n):
seq(a(n), n=0..20);
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MATHEMATICA
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s[n_] := s[n] = If[n < 4, {1, 1, 2t, 4t + 2 t^2}[[n+1]], Expand[(n+1-t)* s[n-1] - (1-t)(n-2 + 3t) s[n-2] - (1-t)^2 (n-5+t) s[n-3] + (1-t)^3 (n-3)* s[n-4]]];
a[n_] := Coefficient[s[2n], t, n];
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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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