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

0,5

Comments

Row sums are:

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

Links

Table of n, a(n) for n=0..61.

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}].

Example

{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}

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[%]

Crossrefs

A060187, A000167

Sequence in context: A176063 A350060 A155467 * A152969 A138076 A060187

Adjacent sequences: A152933 A152934 A152935 * A152937 A152938 A152939

Keyword

nonn,tabl

Author

Roger L. Bagula, Dec 15 2008

Status

approved