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A181992 n-alternating permutations of length n^2.

%I A181992 #14 Aug 12 2019 18:09:21
%S A181992 1,1,5,1513,60376809,613498040952501,2655748106132754540814283,
%T A181992 7350748555338515554166266981278924209,
%U A181992 18155845241010181420704703186769135339279915667193169,53121946985233865823079732996510797894348260342024814486694637630897821
%N A181992 n-alternating permutations of length n^2.
%C A181992 These are the generalized Euler numbers A181985(n, n) and also the André numbers A181937(n, n^2).
%H A181992 Alois P. Heinz, <a href="/A181992/b181992.txt">Table of n, a(n) for n = 0..26</a>
%H A181992 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>
%p A181992 A181992 := proc(n) local E, dim, i, k; dim := n*n;
%p A181992 E := array(0..dim, 0..dim); E[0, 0] := 1;
%p A181992 for i from 1 to dim do
%p A181992 if i mod n = 0 then E[i, 0] := 0 ;
%p A181992    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;
%p A181992 else E[0, i] := 0;
%p A181992    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;
%p A181992 fi od;
%p A181992 E[0, dim] end:
%p A181992 seq(A181992(i),i=0..9);
%t A181992 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 *)
%Y A181992 Cf. A181985, A181937.
%K A181992 nonn
%O A181992 0,3
%A A181992 _Peter Luschny_, Apr 05 2012
%E A181992 a(0)=1 prepended by _Alois P. Heinz_, Aug 12 2019