0,4

Row sums are zero.

First column is A000254 :

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

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},

{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}

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[%]

A000254

Sequence in context: A021333 A104141 A060533 this_sequence A157521 A128252 A033596

Adjacent sequences: A157522 A157523 A157524 this_sequence A157526 A157527 A157528

sign,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 02 2009