0,8

Row sums are:

{1, 2, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800,...}.

This designed symmetrical triangle is meant to be like the Eulerian numbers

in row sum ( the Stirling numbers of the first kind also have factorial row sums).

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

if[ even{1.n,n^2,...,n!-2Sum[2^m,{m,0,n/2-1}],...n^2.n,1}].

{1},

{1, 1},

{1, 0, 1},

{1, 2, 2, 1},

{1, 4, 14, 4, 1},

{1, 5, 54, 54, 5, 1},

{1, 6, 36, 634, 36, 6, 1},

{1, 7, 49, 2463, 2463, 49, 7, 1},

{1, 8, 64, 512, 39150, 512, 64, 8, 1},

{1, 9, 81, 729, 180620, 180620, 729, 81, 9, 1},

{1, 10, 100, 1000, 10000, 3606578, 10000, 1000, 100, 10, 1}

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}], {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}], {n!/2 - Sum[ n^m, {m, 0, Floor[n/2] - 1}], 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[%]

Sequence in context: A121697 A124976 A113021 this_sequence A064552 A123585 A145668

Adjacent sequences: A152934 A152935 A152936 this_sequence A152938 A152939 A152940

nonn,tabl

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 15 2008