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A154913 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]). 0
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; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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# ] &)]

LINKS

Table of n, a(n) for n=0..44.

FORMULA

p = 2; q = 1;

t(n,m) = (p^(n - m)*q^m + p^m*q^(n - m))*(StirlingS1[n, m] + StirlingS1[n, n - m]).

EXAMPLE

{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}

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))*(StirlingS1[n, m] + StirlingS1[n, n - m]);

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

Flatten[%]

CROSSREFS

Sequence in context: A005589 A052360 A263046 * A154915 A238376 A237197

Adjacent sequences:  A154910 A154911 A154912 * A154914 A154915 A154916

KEYWORD

uned,tabl,sign

AUTHOR

Roger L. Bagula, Jan 17 2009

STATUS

approved

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Last modified June 25 23:52 EDT 2019. Contains 324367 sequences. (Running on oeis4.)