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%I #2 Mar 30 2012 17:34:40
%S 1,1,1,1,11,1,1,45,45,1,1,151,459,151,1,1,473,3363,3363,473,1,1,1443,
%T 21085,47095,21085,1443,1,1,4357,121313,519445,519445,121313,4357,1,1,
%U 13103,663223,4970575,9350027,4970575,663223,13103,1,1,39345,3512679
%N A symmetrical triangle of polynomial coefficients:q=2;p(x,n,q)=(1 - x)^(n + 1)*Sum[((q*k + 1)^n + (q*k + q - 1)^n)*x^k, {k, 0, Infinity}]
%C Row sums are:
%C {1, 2, 13, 92, 763, 7674, 92153, 1290232, 20643831, 371589110, 7431782389,...}.
%F q=2;p(x,n,q)=(1 - x)^(n + 1)*Sum[((q*k + 1)^n + (q*k + q - 1)^n)*x^k, {k, 0, Infinity}];
%F t(n,m,2)=coefficients(p(x,n,2))
%e {1},
%e {1, 1},
%e {1, 11, 1},
%e {1, 45, 45, 1},
%e {1, 151, 459, 151, 1},
%e {1, 473, 3363, 3363, 473, 1},
%e {1, 1443, 21085, 47095, 21085, 1443, 1},
%e {1, 4357, 121313, 519445, 519445, 121313, 4357, 1},
%e {1, 13103, 663223, 4970575, 9350027, 4970575, 663223, 13103, 1},
%e {1, 39345, 3512679, 43415943, 138826587, 138826587, 43415943, 3512679, 39345, 1},
%e {1, 118075, 18232281, 356601807, 1813846563, 3054184935, 1813846563, 356601807, 18232281, 118075, 1}
%t p[x_, n_, q_] = (1 - x)^(n + 1)* Sum[((q*k + 1)^n + (q*k + q - 1)^n)*x^k, {k, 0, Infinity}];
%t f[n_, m_, q_] := CoefficientList[FullSimplify[ExpandAll[p[x, n, q]]], x][[m + 1]];
%t Table[Flatten[Table[Table[FullSimplify[ ExpandAll[f[ n, m, q] - f[n, 0, q] + 1]], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]
%Y Cf. A008518, A174599
%K nonn,tabl,uned
%O 0,5
%A _Roger L. Bagula_, Apr 11 2010
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