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Search: id:A154914
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| A154914 |
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A triangular sequence: p = 2; q = 3; t(n,m) = (p^(n - m)*q^m + p^m*q^( n - m))*(StirlingS1[n, m] + StirlingS1[n, n - m]). |
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| 4, 5, 5, 13, -24, 13, 35, -30, -30, 35, 97, -936, 1584, -936, 97, 275, 2940, -2700, -2700, 2940, 275, 793, -78570, 168012, -194400, 168012, -78570, 793, 2315, 1153350, -2002140, 960120, 960120, -2002140, 1153350, 2315, 6817, -24113544
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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Row sums are:
{4, 10, 2, 10, -94, 1030, -13930, 227290, -4363870, 96566470, -2422269850,..}.
Fractal Plot:
a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 243}];
b = Table[If[m <= n, 5 - Mod[a[[n]][[m]], 5], 0], {m, 1, Length[a]}, {n, 1, Length[a]}];
ListDensityPlot[b, Mesh -> False, Frame -> False, AspectRatio -> Automatic, ColorFunction -> (Hue[2# ] &)]
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FORMULA
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p = 2; q = 3;
t(n,m) = (p^(n - m)*q^m + p^m*q^(n - m))*(StirlingS1[n, m] + StirlingS1[n, n - m]).
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EXAMPLE
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{4},
{5, 5},
{13, -24, 13},
{35, -30, -30, 35},
{97, -936, 1584, -936, 97},
{275, 2940, -2700, -2700, 2940, 275},
{793, -78570, 168012, -194400, 168012, -78570, 793},
{2315, 1153350, -2002140, 960120, 960120, -2002140, 1153350, 2315},
{6817, -24113544, 46757880, -42378336, 35090496, -42378336, 46757880, -24113544, 6817},
{20195, 559544760, -1079476200, 858725280, -290530800, -290530800, 858725280, -1079476200, 559544760, 20195},
{60073, -14844358350, 29331528408, -24768406800, 13258584144, -8377084800, 13258584144, -24768406800, 29331528408, -14844358350, 60073}
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MATHEMATICA
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Clear[t, p, q, n, m, a];
p = 2; q = 3;
t[n_, m_] = (p^(n - m)*q^m + p^m*q^(n - m))*(StirlingS1[n, m] + StirlingS1[n, n - m]);
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A154857 A019314 A120132 this_sequence A154916 A077061 A072508
Adjacent sequences: A154911 A154912 A154913 this_sequence A154915 A154916 A154917
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 17 2009
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