1,3

Row sums are:A000680;-(2*n)!/2^n;

{-1, -6, -90, -2520, -113400, -7484400, -681080400, -81729648000,

-12504636144000, -2375880867360000,...}

p(x,n)=(x - 1)^(2*n + 1)*Sum[(k*(k + 1)/2)^n*x^k, {k, 0, Infinity}]/x;

t(n,m)=Coefficients(p(x,n)).

{-1},

{-1, -4, -1},

{-1, -20, -48, -20, -1},

{-1, -72, -603, -1168, -603, -72, -1},

{-1, -232, -5158, -27664, -47290, -27664, -5158, -232, -1},

{-1, -716, -37257, -450048, -1822014, -2864328, -1822014, -450048, -37257, -716, -1},

{-1, -2172, -247236, -6030140, -49258935, -163809288, -242384856, -163809288, -49258935, -6030140, -247236, -2172, -1},

{-1, -6544, -1568215, -72338144, -1086859301, -6727188848, -19323413187, -27306899520, -19323413187, -6727188848, -1086859301, -72338144, -1568215, -6544, -1},

{-1, -19664, -9703890, -811888600, -21147576440, -225167210712, -1130781824398, -2898916824320, -3950966047950, -2898916824320, -1130781824398, -225167210712, -21147576440, -811888600, -9703890, -19664, -1},

{-1, -59028, -59226357, -8742609264, -379269758400, -6590156148912, -54076536713976, -230479103253264, -539417838175698, -713977455470200, -539417838175698, -230479103253264, -54076536713976, -6590156148912, -379269758400, -8742609264, -59226357, -59028, -1}

Clear[p, x, n]; p[x_, n_] = (x - 1)^(2*n + 1)*Sum[(k*(k + 1)/2)^n*x^k, {k, 0, Infinity}]/x;

Table[FullSimplify[ExpandAll[p[x, n]]], {n, 1, 10}];

Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 1, 10}];

Flatten[%]

A000680

Sequence in context: A034802 A139167 A156586 this_sequence A015113 A016519 A113716

Adjacent sequences: A154280 A154281 A154282 this_sequence A154284 A154285 A154286

sign,tabl,uned,tabl

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 06 2009