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A181992 n-alternating permutations of length n^2. 2
1, 1, 5, 1513, 60376809, 613498040952501, 2655748106132754540814283, 7350748555338515554166266981278924209, 18155845241010181420704703186769135339279915667193169, 53121946985233865823079732996510797894348260342024814486694637630897821 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

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 *)

CROSSREFS

Cf. A181985, A181937.

Sequence in context: A317731 A259867 A169620 * A145694 A184970 A184973

Adjacent sequences:  A181989 A181990 A181991 * A181993 A181994 A181995

KEYWORD

nonn

AUTHOR

Peter Luschny, Apr 05 2012

EXTENSIONS

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

STATUS

approved

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Last modified June 12 23:09 EDT 2021. Contains 344978 sequences. (Running on oeis4.)