A154816 - OEIS

%I #2 Mar 30 2012 17:34:29

%S 2,5,5,17,66,17,65,685,685,65,257,6572,16342,6572,257,1025,60675,

%T 313300,313300,60675,1025,4097,549418,5340455,10712060,5340455,549418,

%U 4097,16385,4931825,84856215,303945575,303945575,84856215,4931825,16385

%N A triangular sequence of polynomial coefficients: p(x,n)=((-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(5*m + 4)^n*x^m, {m, 0, Infinity}] + (-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(5*m + 1)^n*x^m, {m, 0, Infinity}]).

%C Row sums are:

%C {2, 10, 100, 1500, 30000, 750000, 22500000, 787500000, 31500000000,

%C 1417500000000, 70875000000000}

%F p(x,n)=((-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(5*m + 4)^n*x^m, {m, 0, Infinity}] +

%F (-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(5*m + 1)^n*x^m, {m, 0, Infinity}]);

%F t(n,m)=coefficients(p(x,n))

%e {2},

%e {5, 5},

%e {17, 66, 17},

%e {65, 685, 685, 65},

%e {257, 6572, 16342, 6572, 257},

%e {1025, 60675, 313300, 313300, 60675, 1025},

%e {4097, 549418, 5340455, 10712060, 5340455, 549418, 4097},

%e {16385, 4931825, 84856215, 303945575, 303945575, 84856215, 4931825, 16385},

%e {65537, 44136504, 1289970236, 7671841928, 13487971590, 7671841928, 1289970236, 44136504, 65537},

%e {262145, 394876735, 19055809150, 179073190690, 510225861280, 510225861280, 179073190690, 19055809150, 394876735, 262145},

%e {1048577, 3535716230, 276229994965, 3958390776760, 17297519264170, 27803646398596, 17297519264170, 3958390776760, 276229994965, 3535716230, 1048577}

%t Clear[p]; p[x_, n_] = ((-1)^( n + 1)*(x - 1)^(n + 1)*Sum[(5*m + 4)^n*x^m, {m, 0, Infinity}] +

%t (-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(5*m + 1)^n*x^m, {m, 0, Infinity}]);

%t Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];

%t Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];

%t Flatten[%]

%K nonn,tabl,uned

%O 0,1

%A _Roger L. Bagula_, Jan 15 2009