A229886 Number of 5 up, 5 down permutations of [n].

1, 1, 1, 1, 1, 1, 1, 6, 21, 56, 126, 252, 2562, 14442, 59487, 199627, 578005, 8330800, 65056960, 363823800, 1628423880, 6190034016, 115452938151, 1152005977431, 8137667253101, 45527993728141, 214265281290061, 4904624749585886, 59578069604921361

Offset: 0

Author

Alois P. Heinz, Oct 02 2013

Keywords

• nonn
• eigen

Comments

Limit n->infinity (a(n)/n!)^(1/n) = 0.337596001995... . - Vaclav Kotesovec, Sep 06 2014

Examples

			a(6) = 1: 123456.
a(7) = 6: 1234576, 1234675, 1235674, 1245673, 1345672, 2345671.
a(8) = 21: 12345876, 12346875, 12347865, 12356874, 12357864, 12367854, 12456873, 12457863, 12467853, 12567843, 13456872, 13457862, 13467852, 13567842, 14567832, 23456871, 23457861, 23467851, 23567841, 24567831, 34567821.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..545

Crossrefs

Column k=5 of A229892.

Programs

Maple

b:= proc(u, o, t) option remember; `if`(u+o=0, 1, add(`if`(t=5,
       b(o-j, u+j-1, 1), b(u+j-1, o-j, t+1)), j=1..o))
    end:
a:= n-> b(0, n, 0):
seq(a(n), n=0..35);

Mathematica

b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, Sum[If[t == 5, b[o - j, u + j - 1, 1], b[u + j - 1, o - j, t + 1]], {j, 1, o}]];
a[n_] := b[0, n, 0];
a /@ Range[0, 35] (* Jean-François Alcover, Dec 22 2020, after Alois P. Heinz *)