A181992 n-alternating permutations of length n^2.

1, 1, 5, 1513, 60376809, 613498040952501, 2655748106132754540814283, 7350748555338515554166266981278924209, 18155845241010181420704703186769135339279915667193169, 53121946985233865823079732996510797894348260342024814486694637630897821

Offset: 0

Author

Peter Luschny, Apr 05 2012

Keywords

• nonn

Comments

These are the generalized Euler numbers A181985(n, n) and also the André numbers A181937(n, n^2).

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..26
• Peter Luschny, An old operation on sequences: the Seidel transform

Crossrefs

Cf. A181985, A181937.

Programs

Maple

A181992 := proc(n) local E, dim, i, k; dim := n*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(A181992(i),i=0..9);

Mathematica

A181985[n_, len_] := Module[{e, dim = n*(len - 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]]]]; Table[e[0, n*k], {k, 0, len - 1}]]; a[n_] := A181985[n, n + 1][[n + 1]]; Table[a[n], {n, 1, 14}] (* Jean-François Alcover, Dec 17 2013, after Maple code in A181985 *)

Extensions

a(0)=1 prepended by Alois P. Heinz, Aug 12 2019