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A154914 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]). 0
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; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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# ] &)]

LINKS

Table of n, a(n) for n=0..37.

FORMULA

p = 2; q = 3;

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

EXAMPLE

{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}

MATHEMATICA

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[%]

CROSSREFS

Sequence in context: A019314 A195598 A120132 * A154916 A077061 A072508

Adjacent sequences:  A154911 A154912 A154913 * A154915 A154916 A154917

KEYWORD

uned,tabl,sign

AUTHOR

Roger L. Bagula, Jan 17 2009

STATUS

approved

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Last modified June 24 17:58 EDT 2019. Contains 324330 sequences. (Running on oeis4.)