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A211213 n-alternating permutations of length 3n. 4
1, 61, 1513, 33661, 750751, 17116009, 398840401, 9464040829, 227864057851, 5550936701311, 136526608389601, 3384729259165801, 84478081828015513, 2120572560190269841, 53494979095639780513, 1355345459896317255037, 34469858667289041256051, 879619727291950363099291 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..18.

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

FORMULA

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

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 *)

CROSSREFS

Cf. A181985, A030662, A181991.

Sequence in context: A060061 A000507 A143011 * A229667 A242382 A017777

Adjacent sequences:  A211210 A211211 A211212 * A211214 A211215 A211216

KEYWORD

nonn

AUTHOR

Peter Luschny, Apr 05 2012

STATUS

approved

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Last modified November 30 13:12 EST 2021. Contains 349419 sequences. (Running on oeis4.)