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A154915 A triangular sequence: p = 2; q = 1; t(n,m) = (p^(n - m)*q^m + p^m*q^( n - m))*(StirlingS2[n, m] + StirlingS2[n, n - m]). 0
4, 3, 3, 5, 8, 5, 9, 24, 24, 9, 17, 70, 112, 70, 17, 33, 198, 480, 480, 198, 33, 65, 544, 1920, 2880, 1920, 544, 65, 129, 1452, 7308, 15624, 15624, 7308, 1452, 129, 257, 3770, 26724, 80640, 108864, 80640, 26724, 3770, 257, 513, 9546, 94644, 408312, 706608 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are:

{4, 6, 18, 66, 286, 1422, 7938, 49026, 331646, 2439246, 19394498,..}.

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# ] &)]

LINKS

Table of n, a(n) for n=0..49.

FORMULA

p = 2; q = 1;

t(n,m) = (p^(n - m)*q^m + p^m*q^(n - m))*(StirlingS2[n, m] + StirlingS2[n, n - m]).

EXAMPLE

{4},

{3, 3},

{5, 8, 5},

{9, 24, 24, 9},

{17, 70, 112, 70, 17},

{33, 198, 480, 480, 198, 33},

{65, 544, 1920, 2880, 1920, 544, 65},

{129, 1452, 7308, 15624, 15624, 7308, 1452, 129},

{257, 3770, 26724, 80640, 108864, 80640, 26724, 3770, 257},

{513, 9546, 94644, 408312, 706608, 706608, 408312, 94644, 9546, 513},

{1025, 23644, 327860, 2068560, 4554560, 5443200, 4554560, 2068560, 327860, 23644, 1025}

MATHEMATICA

Clear[t, p, q, n, m, a];

p = 2; q = 1;

t[n_, m_] = (p^(n - m)*q^m + p^m*q^(n - m))*(StirlingS2[n, m] + StirlingS2[n, n - m]);

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A052360 A263046 A154913 * A238376 A237197 A006994

Adjacent sequences:  A154912 A154913 A154914 * A154916 A154917 A154918

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Jan 17 2009

STATUS

approved

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Last modified June 19 05:30 EDT 2019. Contains 324218 sequences. (Running on oeis4.)