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Search: id:A154913
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| A154913 |
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A triangular sequence: p = 2; q = 1; 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, 3, 3, 5, -8, 5, 9, -6, -6, 9, 17, -120, 176, -120, 17, 33, 252, -180, -180, 252, 33, 65, -4590, 7180, -7200, 7180, -4590, 65, 129, 46134, -57204, 21336, 21336, -57204, 46134, 129, 257, -658840, 910520, -603680, 433216, -603680, 910520, -658840, 257
(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, 6, 2, 6, -30, 210, -1890, 20790, -270270, 4054050, -68918850,..}.
Fractal Plot:
a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 243}];
b = Table[If[m <= n, 3 - Mod[a[[n]][[m]], 3], 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 = 1;
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},
{3, 3},
{5, -8, 5},
{9, -6, -6, 9},
{17, -120, 176, -120, 17},
{33, 252, -180, -180, 252, 33},
{65, -4590, 7180, -7200, 7180, -4590, 65},
{129, 46134, -57204, 21336, 21336, -57204, 46134, 129},
{257, -658840, 910520, -603680, 433216, -603680, 910520, -658840, 257},
{513, 10393272, -14393016, 8178336, -2152080, -2152080, 8178336, -14393016, 10393272, 513},
{1025, -186543450, 267135960, -160772400, 62956240, -34473600, 62956240, -160772400, 267135960, -186543450, 1025}
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MATHEMATICA
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Clear[t, p, q, n, m, a];
p = 2; q = 1;
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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Adjacent sequences: A154910 A154911 A154912 this_sequence A154914 A154915 A154916
Sequence in context: A063571 A005589 A052360 this_sequence A154915 A006994 A038627
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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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