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A157525 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])). 0
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; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are zero.

First column is A000254 :

{0, 1, 3, 11, 50, 274, 1764, 13068, 109584, 1026576, 10628640....}.

LINKS

Table of n, a(n) for n=0..45.

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])).

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}

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[%]

CROSSREFS

A000254

Sequence in context: A212036 A191619 A327245 * A157521 A176005 A211963

Adjacent sequences:  A157522 A157523 A157524 * A157526 A157527 A157528

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Mar 02 2009

STATUS

approved

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Last modified December 1 13:22 EST 2021. Contains 349429 sequences. (Running on oeis4.)