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%I #12 Aug 13 2015 14:50:29
%S 1,61,1513,33661,750751,17116009,398840401,9464040829,227864057851,
%T 5550936701311,136526608389601,3384729259165801,84478081828015513,
%U 2120572560190269841,53494979095639780513,1355345459896317255037,34469858667289041256051,879619727291950363099291
%N n-alternating permutations of length 3n.
%C a(n) = A181985(n,3).
%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>
%F a(n) = (3*n)!*(1/(3*n)!-2/(n!*(2*n)!)+1/(n!)^3). - _Peter Luschny_, Aug 13 2015
%p A211213 := proc(n) local E, dim, i, k; dim := 3*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; E[0, dim] end:
%p seq(A211213(n), n = 1..18);
%p # Alternatively:
%p a := x -> (3*x)!*(1/(3*x)!-2/(x!*(2*x)!)+1/(x!)^3):
%p seq(a(n),n=1..18); # _Peter Luschny_, Aug 13 2015
%t 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 *)
%Y Cf. A181985, A030662, A181991.
%K nonn
%O 1,2
%A _Peter Luschny_, Apr 05 2012
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