A320290 Number of permutations p of [2n] such that in 0p the largest up-jump equals n and no down-jump is larger than 2.

1, 1, 9, 156, 3098, 69274, 1626122, 39892080, 1004867492, 25886899652, 677767802220, 17984050212906, 482214668573802, 13042214648300918, 355247290177412584, 9733704443846822462, 268026951144933433138, 7411550898419782031320, 205686202884689885529314

Offset: 0

Author

Alois P. Heinz, Oct 27 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A291680.

Programs

Maple

b:= proc(u, o, k) option remember; `if`(u+o=0, 1,
      add(b(u-j, o+j-1, k), j=1..min(2, u))+
      add(b(u+j-1, o-j, k), j=1..min(k, o)))
    end:
a:= n-> `if`(n=0, 1, b(0, 2*n, n)-b(0, 2*n, n-1)):
seq(a(n), n=0..20);

Mathematica

b[u_, o_, k_] := b[u, o, k] = If[u + o == 0, 1,
     Sum[b[u - j, o + j - 1, k], {j, 1, Min[2, u]}] +
     Sum[b[u + j - 1, o - j, k], {j, 1, Min[k, o]}]];
a[n_] := If[n == 0, 1, b[0, 2*n, n] - b[0, 2*n, n - 1]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Apr 21 2022, after Alois P. Heinz *)

Formula

a(n) = A291680(2n,n).