A181992 - OEIS

%I #14 Aug 12 2019 18:09:21

%S 1,1,5,1513,60376809,613498040952501,2655748106132754540814283,

%T 7350748555338515554166266981278924209,

%U 18155845241010181420704703186769135339279915667193169,53121946985233865823079732996510797894348260342024814486694637630897821

%N n-alternating permutations of length n^2.

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

%H Alois P. Heinz, <a href="/A181992/b181992.txt">Table of n, a(n) for n = 0..26</a>

%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>

%p A181992 := proc(n) local E, dim, i, k; dim := n*n;

%p E := array(0..dim, 0..dim); E[0, 0] := 1;

%p for i from 1 to dim do

%p if i mod n = 0 then E[i, 0] := 0 ;

%p    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 else E[0, i] := 0;

%p    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 fi od;

%p E[0, dim] end:

%p seq(A181992(i),i=0..9);

%t 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 Cf. A181985, A181937.

%K nonn

%O 0,3

%A _Peter Luschny_, Apr 05 2012

%E a(0)=1 prepended by _Alois P. Heinz_, Aug 12 2019