|
Search: id:A154916
|
|
|
| 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
1
|
|
| 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; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
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# ] &)]
|
|
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: A019314 A120132 A154914 this_sequence A077061 A072508 A075566
Adjacent sequences: A154913 A154914 A154915 this_sequence A154917 A154918 A154919
|
|
KEYWORD
|
nonn,tabl,uned,tabl
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 17 2009
|
|
|
Search completed in 0.002 seconds
|
