A176160 - OEIS

%I #2 Mar 30 2012 17:34:40

%S 1,5,5,25,81,25,125,2197,2197,125,625,83521,390625,83521,625,3125,

%T 4084101,115856201,115856201,4084101,3125,15625,244140625,51520374361,

%U 282429536481,51520374361,244140625,15625,78125,17249876309

%N A polynomial coefficient sequence:p(x,n,m)=(1 + 4*Binomial[n, m]*x)^n

%C Row sums are:

%C {1, 10, 131, 4644, 558917, 239886854, 385958597703, 2280119446470280, 52063212260725437065, 4384388899674032467912458, 1449048908960986942519336016459,...}.

%F p(x,n,m)=(1 + 4*Binomial[n, m]*x)^n

%e {1},

%e {5, 5},

%e {25, 81, 25},

%e {125, 2197, 2197, 125},

%e {625, 83521, 390625, 83521, 625},

%e {3125, 4084101, 115856201, 115856201, 4084101, 3125},

%e {15625, 244140625, 51520374361, 282429536481, 51520374361, 244140625, 15625},

%e {78125, 17249876309, 32057708828125, 1107984764452581, 1107984764452581, 32057708828125, 17249876309, 78125},

%e {390625, 1406408618241, 26584441929064321, 6568408355712890625, 38873223852623509441, 6568408355712890625, 26584441929064321, 1406408618241, 390625},

%e {1953125, 129961739795077, 28334269484119140625, 56062067225927988301777, 2136104048211642384765625, 2136104048211642384765625, 56062067225927988301777, 28334269484119140625, 129961739795077, 1953125},

%e {9765625, 13422659310152401, 37738596846955704499801, 662904189510194816788612801, 176994576151109753197786640401, 1093733872802526507260136674401, 176994576151109753197786640401, 662904189510194816788612801, 37738596846955704499801, 13422659310152401, 9765625}

%t Clear[p, n, m];

%t p[x_, n_, m_] := (1 + 4*Binomial[n, m]*x)^n;

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

%t Flatten[%]

%K nonn,tabl,uned

%O 0,2

%A _Roger L. Bagula_, Apr 10 2010