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Search: id:A152972
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| A152972 |
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A vector sequence with set row sum function: row(n)=-Product[3*k - 1, {k, 0, n}] and linear build up and decline function: f(n,m)=Floor[(m/n)*row(n)]. |
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1
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| 1, 1, 1, 1, 8, 1, 1, 39, 39, 1, 1, 110, 658, 110, 1, 1, 1232, 4927, 4927, 1232, 1, 1, 17453, 34906, 104720, 34906, 17453, 1, 1, 299200, 598400, 1196799, 1196799, 598400, 299200, 1, 1, 6021400, 12042800, 18064200, 24085598, 18064200, 12042800
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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row sums -Product[3*k - 1, {k, 0, n}]:A008544
{1, 2, 10, 80, 880, 12320, 209440, 4188800, 96342400, 2504902400, 72642169600,
2324549427200, 81359229952000, 3091650738176000, 126757680265216000,
5577337931669504000, 262134882788466688000, 13106744139423334400000,
694657439389436723200000,...}
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FORMULA
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row(n)=(2*n)!/n!: f(n,m)=Floor[(m/n)*row(n)].
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EXAMPLE
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{1},
{1, 1},
{1, 8, 1},
{1, 39, 39, 1},
{1, 110, 658, 110, 1},
{1, 1232, 4927, 4927, 1232, 1},
{1, 17453, 34906, 104720, 34906, 17453, 1},
{1, 299200, 598400, 1196799, 1196799, 598400, 299200, 1},
{1, 6021400, 12042800, 18064200, 24085598, 18064200, 12042800, 6021400, 1},
{1, 139161244, 278322488, 417483733, 417483734, 417483734, 417483733, 278322488, 139161244, 1},
{1, 3632108480, 7264216960, 10896325440, 14528433920, -2, 14528433920, 10896325440, 7264216960, 3632108480, 1}
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MATHEMATICA
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Clear[v, n, row, f]; row[n_] = -Product[3*k - 1, {k, 0, n}];
f[n_, m_] = Floor[(m/n)*row[n]/2]; v[0] = {1}; v[1] = {1, 1};
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}],
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}]];
Table[FullSimplify[v[n]], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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A008544, A142458, A142459
Sequence in context: A142175 A142597 A156137 this_sequence A166346 A157640 A142458
Adjacent sequences: A152969 A152970 A152971 this_sequence A152973 A152974 A152975
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 16 2008
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