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%I #3 Mar 30 2012 17:34:28
%S 1,1,1,1,10,1,1,59,59,1,1,210,1258,210,1,1,3024,12095,12095,3024,1,1,
%T 55440,110880,332638,110880,55440,1,1,1235520,2471040,4942079,4942079,
%U 2471040,1235520,1,1,32432400,64864800,97297200,129729598,97297200
%N A vector sequence with set row sum function: row(n)=(2*n)!/n! and linear build up and decline function: f(n,m)=Floor[(m/n)*row(n)].
%C row sums (2*n)!/n!:
%C {1, 2, 12, 120, 1680, 30240, 665280, 17297280, 518918400, 17643225600, 67044257280,...}
%F row(n)=(2*n)!/n!: f(n,m)=Floor[(m/n)*row(n)].
%e {1},
%e {1, 1},
%e {1, 10, 1},
%e {1, 59, 59, 1},
%e {1, 210, 1258, 210, 1},
%e {1, 3024, 12095, 12095, 3024, 1},
%e {1, 55440, 110880, 332638, 110880, 55440, 1},
%e {1, 1235520, 2471040, 4942079, 4942079, 2471040, 1235520, 1},
%e {1, 32432400, 64864800, 97297200, 129729598, 97297200, 64864800, 32432400, 1},
%e {1, 980179200, 1960358400, 2940537600, 2940537599, 2940537599, 2940537600, 1960358400, 980179200, 1},
%e {1, 33522128640, 67044257280, 100566385920, 134088514560, -2, 134088514560, 100566385920, 67044257280, 33522128640, 1}
%t Clear[v, n, row, f]; row[n_] = (2*n)!/n!;
%t f[n_, m_] = Floor[(m/n)*row[n]/2]; v[0] = {1}; v[1] = {1, 1};
%t v[n_] := v[n] = If[Mod[n, 2] == 0, Join[{1}, Table[ f[n, m], {m, 1, Floor[ n/2] - 1}], {row[n] - 2*Sum[ f[n, m], {m, 1, Floor[n/2] - 1}] - 2}, Table[ f[n, m], {m, Floor[n/ 2] - 1, 1, -1}], { 1}],
%t Join[{1}, Table[ f[n, m], {m, 1, Floor[n/2] - 1}], {row[n]/2 - Sum[ f[n, m], { m, 1, Floor[n/2] - 1}] - 1, row[n]/ 2 - Sum[ f[n, m], {m, 1, Floor[ n/2] - 1}] - 1}, Table[ f[n, m], {m, Floor[n/ 2] - 1, 1, -1}], {1}]];
%t Table[v[n], {n, 0, 10}]; Flatten[%]
%Y A142459
%K nonn,tabl,uned
%O 0,5
%A _Roger L. Bagula_, Dec 16 2008
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