A152936 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}].
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, 6, 1, 1, 7, 49, 322503, 322503, 49, 7, 1, 1, 8, 64, 512, 10320750, 512, 64, 8, 1, 1, 9, 81, 729, 92896460, 92896460, 729, 81, 9, 1, 1, 10, 100, 1000, 10000, 3715868978, 10000
Offset: 0
Examples
{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, 6, 1},
{1, 7, 49, 322503, 322503, 49, 7, 1},
{1, 8, 64, 512, 10320750, 512, 64, 8, 1},
{1, 9, 81, 729, 92896460, 92896460, 729, 81, 9, 1},
{1, 10, 100, 1000, 10000, 3715868978, 10000, 1000, 100, 10, 1}
Programs
-
Mathematica
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}]], 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}]]]' Table[v[n], {n, 0, 10}]; Flatten[%]
Formula
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}].
Comments