_Roger L. Bagula (rlbagulatftn(AT)yahoo.com), _, Apr 11 2010

A sequence of polynomial coefficients:p(x,n,m)=(1 + (Binomial[n, m]*Binomial[n + 1, m]/(m + 1))*x)^n

1, 2, 2, 4, 16, 4, 8, 343, 343, 8, 16, 14641, 194481, 14641, 16, 32, 1048576, 345025251, 345025251, 1048576, 32, 64, 113379904, 1418519112256, 29721861554176, 1418519112256, 113379904, 64, 128, 17249876309, 11514990476898413

0,2

Row sums are :

{1, 4, 24, 702, 223795, 692147718, 32559126538624, 13782459932899570762,

101546283389149890712153383, 6529719086356437527412019094222406,

8094296318445604076821089587379253402373981,...}

p(x,n,m)=(1 + (Binomial[n, m]*Binomial[n + 1, m]/(m + 1))*x)^n

{1},

{2, 2},

{4, 16, 4},

{8, 343, 343, 8},

{16, 14641, 194481, 14641, 16},

{32, 1048576, 345025251, 345025251, 1048576, 32},

{64, 113379904, 1418519112256, 29721861554176, 1418519112256, 113379904, 64},

{128, 17249876309, 11514990476898413, 6879714958723010531, 6879714958723010531, 11514990476898413, 17249876309, 128},

{256, 3512479453921, 166356282569519253121, 3683084668584351607174081, 94179781339409023500390625, 3683084668584351607174081, 166356282569519253121, 3512479453921, 256},

{512, 922190162669056, 3969861779162915894438461, 4112970656406400927417840669081, 3260746568551950582693485649334093, 3260746568551950582693485649334093, 4112970656406400927417840669081, 3969861779162915894438461, 922190162669056, 512},

{1024, 303305489096114176, 147842900128430337645756261376, 8849714563860555567244518171900162001, 261785528590768429087763042357778928140601, 7570707561834643811734171546341082041015625, 261785528590768429087763042357778928140601, 8849714563860555567244518171900162001, 147842900128430337645756261376, 303305489096114176, 1024}

p[x_, n_, m_] := (1 + (Binomial[n, m]*Binomial[n + 1, m]/(m + 1))*x)^n

Table[Table[Apply[Plus, CoefficientList[p[x, n, m], x]], {m, 0, n}], {n, 0, 10}];

Flatten[%]

nonn,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 11 2010

approved