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A303203
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Number of permutations p of [2n+1] such that 0p has a nonincreasing jump sequence beginning with n+1.
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3
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1, 2, 12, 98, 988, 10872, 129520, 1609176, 20786804, 274792342, 3719296036, 51119572738, 712918642042, 10055531355652, 143287150725298, 2058368140071146, 29796314629826814, 434051906728752164, 6359063811707227298, 93635249115751389952, 1385028309353547034876
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OFFSET
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0,2
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COMMENTS
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An up-jump j occurs at position i in p if p_{i} > p_{i-1} and j is the index of p_i in the increasingly sorted list of those elements in {p_{i}, ..., p_{n}} that are larger than p_{i-1}. A down-jump j occurs at position i in p if p_{i} < p_{i-1} and j is the index of p_i in the decreasingly sorted list of those elements in {p_{i}, ..., p_{n}} that are smaller than p_{i-1}. First index in the lists is 1 here.
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LINKS
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FORMULA
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MAPLE
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b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
add(b(sort([u-j, o+j-1])[], j), j=1..min(t, u))+
add(b(sort([u+j-1, o-j])[], j), j=1..min(t, o)))
end:
a:= n-> b(0, 2*n+1, n+1)-b(0, 2*n+1, n):
seq(a(n), n=0..25);
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MATHEMATICA
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b[u_, o_, t_] := b[u, o, t] = If[u+o == 0, 1,
Sum[b[u-j, o+j-1, j], {j, 1, Min[t, u]}] +
Sum[b[u+j-1, o-j, j], {j, 1, Min[t, o]}]];
a[n_] := b[0, 2n+1, n+1] - b[0, 2n+1, 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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