A211213 n-alternating permutations of length 3n.

1, 61, 1513, 33661, 750751, 17116009, 398840401, 9464040829, 227864057851, 5550936701311, 136526608389601, 3384729259165801, 84478081828015513, 2120572560190269841, 53494979095639780513, 1355345459896317255037, 34469858667289041256051, 879619727291950363099291

Offset: 1

Author

Peter Luschny, Apr 05 2012

Keywords

• nonn

Comments

a(n) = A181985(n,3).

Links

• Peter Luschny, An old operation on sequences: the Seidel transform

Crossrefs

Cf. A181985, A030662, A181991.

Programs

Maple

A211213 := proc(n) local E, dim, i, k; dim := 3*n;
E := array(0..dim, 0..dim); E[0, 0] := 1;
for i from 1 to dim do
if i mod n = 0 then E[i, 0] := 0 ;
   for k from i-1 by -1 to 0 do E[k, i-k] := E[k+1, i-k-1] + E[k, i-k-1] od;
else E[0, i] := 0;
   for k from 1 by 1 to i do E[k, i-k] := E[k-1, i-k+1] + E[k-1, i-k] od;
fi od; E[0, dim] end:
seq(A211213(n), n = 1..18);
# Alternatively:
a := x -> (3*x)!*(1/(3*x)!-2/(x!*(2*x)!)+1/(x!)^3):
seq(a(n),n=1..18); # Peter Luschny, Aug 13 2015

Mathematica

nmax = 18; a[n_] := Module[{e, dim = n*(nmax-1)}, e[0, 0] = 1; For[i = 1, i <= dim, i++, If[Mod[i, n] == 0 , e[i, 0] = 0; For[k = i-1, k >= 0, k--, e[k, i-k] = e[k+1, i-k-1] + e[k, i-k-1] ], e[0, i] = 0; For[k = 1, k <= i, k++, e[k, i-k] = e[k-1, i-k+1] + e[k-1, i-k] ] ]]; e[0, 3*n]] ; Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Jul 26 2013, after Maple *)

Formula

a(n) = (3*n)!*(1/(3*n)!-2/(n!*(2*n)!)+1/(n!)^3). - Peter Luschny, Aug 13 2015