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A157525
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A triangular function: t(x,y)=y!*D[Gamma[y + 1]/(Gamma[x + 1]*Gamma[y - x + 1]), {x, 1}]/(Gamma[y + 1]/(Gamma[x + 1]*Gamma[y - x + 1])).
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0
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0, 1, -1, 3, 0, -3, 11, 3, -3, -11, 50, 20, 0, -20, -50, 274, 130, 40, -40, -130, -274, 1764, 924, 420, 0, -420, -924, -1764, 13068, 7308, 3948, 1260, -1260, -3948, -7308, -13068, 109584, 64224, 38304, 18144, 0, -18144, -38304, -64224, -109584, 1026576
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Row sums are zero.
First column is A000254 :
{0, 1, 3, 11, 50, 274, 1764, 13068, 109584, 1026576, 10628640....}.
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FORMULA
| t(x,y)=y!*D[Gamma[y + 1]/(Gamma[x + 1]*Gamma[y - x + 1]), {x, 1}]/(Gamma[y + 1]/(Gamma[x + 1]*Gamma[y - x + 1])).
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EXAMPLE
| {0},
{1, -1},
{3, 0, -3},
{11, 3, -3, -11},
{50, 20, 0, -20, -50},
{274, 130, 40, -40, -130, -274},
{1764, 924, 420, 0, -420, -924, -1764},
{13068, 7308, 3948, 1260, -1260, -3948, -7308, -13068},
{109584, 64224, 38304, 18144, 0, -18144, -38304, -64224, -109584},
{1026576, 623376, 396576, 223776, 72576, -72576, -223776, -396576, -623376, -1026576},
{10628640, 6636960, 4419360, 2756160, 1330560, 0, -1330560, -2756160, -4419360, -6636960, -10628640}
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MATHEMATICA
| f[x_, y_] = Gamma[y + 1]/(Gamma[x + 1]*Gamma[y - x + 1]);
g[x_, y_] = D[f[x, y], {x, 1}];
a = Table[Table[Rationalize[N[y!*g[x, y]/f[x, y]]], {x, 0, y}], {y, 0, 10}];
Flatten[%]
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CROSSREFS
| A000254
Sequence in context: A060533 A177785 A191619 * A157521 A176005 A128252
Adjacent sequences: A157522 A157523 A157524 * A157526 A157527 A157528
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KEYWORD
| sign,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 02 2009
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