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A154916 A triangular sequence: p = 2; q = 3; t(n,m) = (p^(n - m)*q^m + p^m*q^( n - m))*(StirlingS2[n, m] + StirlingS2[n, n - m]). 0
4, 5, 5, 13, 24, 13, 35, 120, 120, 35, 97, 546, 1008, 546, 97, 275, 2310, 7200, 7200, 2310, 275, 793, 9312, 44928, 77760, 44928, 9312, 793, 2315, 36300, 255780, 703080, 703080, 255780, 36300, 2315, 6817, 137982, 1372356, 5660928, 8817984, 5660928 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are:

{4, 10, 50, 310, 2294, 19570, 187826, 1994950, 23174150, 291794530, 3954319298,..}.

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..41.

FORMULA

p = 2; q = 3;

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

EXAMPLE

{4},

{5, 5},

{13, 24, 13},

{35, 120, 120, 35},

{97, 546, 1008, 546, 97},

{275, 2310, 7200, 7200, 2310, 275},

{793, 9312, 44928, 77760, 44928, 9312, 793},

{2315, 36300, 255780, 703080, 703080, 255780, 36300, 2315},

{6817, 137982, 1372356, 5660928, 8817984, 5660928, 1372356, 137982, 6817},

{20195, 513930, 7098300, 42872760, 95392080, 95392080, 42872760, 7098300, 513930, 20195},

{60073, 1881492, 35999028, 318679920, 959190336, 1322697600, 959190336, 318679920, 35999028, 1881492, 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))*(StirlingS2[n, m] + StirlingS2[n, n - m]);

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

Flatten[%]

CROSSREFS

Sequence in context: A195598 A120132 A154914 * A327703 A077061 A072508

Adjacent sequences:  A154913 A154914 A154915 * A154917 A154918 A154919

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 17 2009

STATUS

approved

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Last modified February 22 05:54 EST 2020. Contains 332116 sequences. (Running on oeis4.)