%I #2 Mar 30 2012 17:34:28

%S 1,1,1,1,6,1,1,23,23,1,1,4,374,4,1,1,5,1914,1914,5,1,1,6,36,45994,36,

%T 6,1,1,7,49,322503,322503,49,7,1,1,8,64,512,10320750,512,64,8,1,1,9,

%U 81,729,92896460,92896460,729,81,9,1,1,10,100,1000,10000,3715868978,10000

%N A vector recursion designed around a row sum of A000165: v(n)=if[odd,{1.n,n^2,...,2^n*n!-Sum2^m,{m,0,n/2-1}],2^n*n!-Sum2^m,{m,0,n/2-1}],...n^2.n,1},{1.n,n^2,...,2^n*n!-2Sum2^m,{m,0,n/2-1}],...n^2.n,1}].

%C Row sums are:

%C {1, 2, 8, 48, 384, 3840, 46080, 645120, 10321920, 185794560, 3715891200,...}

%F v(n)=if[odd,{1.n,n^2,...,2^n*n!-Sum2^m,{m,0,n/2-1}],2^n*n!-Sum2^m,{m,0,n/2-1}],...n^2.n,1},

%F {1.n,n^2,...,2^n*n!-2Sum2^m,{m,0,n/2-1}],...n^2.n,1}].

%e {1},

%e {1, 1},

%e {1, 6, 1},

%e {1, 23, 23, 1},

%e {1, 4, 374, 4, 1},

%e {1, 5, 1914, 1914, 5, 1},

%e {1, 6, 36, 45994, 36, 6, 1},

%e {1, 7, 49, 322503, 322503, 49, 7, 1},

%e {1, 8, 64, 512, 10320750, 512, 64, 8, 1},

%e {1, 9, 81, 729, 92896460, 92896460, 729, 81, 9, 1},

%e {1, 10, 100, 1000, 10000, 3715868978, 10000, 1000, 100, 10, 1}

%t Clear[v, n]; v[0] = {1}; v[1] = {1, 1}; v[n_] := v[n] = If[Mod[n, 2] == 0, Join[Table[ n^m, {m,0, Floor[n/2] - 1}], {2^n*n! - 2*Sum[ n^m, {m, 0, Floor[n/2] - 1}]}, Table[ n^m, {m, Floor[n/2] - 1, 0, -1}]],

%t Join[Table[ n^m, {m, 0, Floor[n/2] - 1}], {2^n*n!/2 - Sum[ n^m, {m, 0,Floor[n/2] - 1}], 2^n*n!/2 - Sum[ n^m, {m, 0, Floor[n/2] - 1}]}, Table[ n^m, {m, Floor[n/2] - 1, 0, -1}]]]'

%t Table[v[n], {n, 0, 10}];

%t Flatten[%]

%Y A060187, A000167

%K nonn,tabl

%O 0,5

%A _Roger L. Bagula_, Dec 15 2008