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%I #6 Jun 22 2015 12:55:33
%S 1,1,1,1,1,1,1,2,2,1,1,3,4,3,1,1,4,8,8,4,1,1,5,12,16,12,5,1,1,6,17,28,
%T 28,17,6,1,1,7,23,45,56,45,23,7,1,1,8,30,68,101,101,68,30,8,1,1,9,38,
%U 98,169,202,169,98,38,9,1,1,10,47,136,267,371,371,267,136,47,10,1
%N A double offset polynomial as a triangle of coefficients: p(x,n)=(x + 1)^n + If[n >= 2, x^2*(x + 1)^(n - 1), x^(n + 1)] + If[n >= 4, x^2*(x + 1)^(n - 3), 0].
%C Row sums are {1, 2, 3, 6, 12, 26, 52, 104, 208, 416, 832, 1664, ...}, A259098.
%F p(x,n)=(x + 1)^n + If[n >= 2, x^2*(x + 1)^(n - 1), x^(n + 1)] + If[n >= 4, x^2*(x + 1)^(n - 3), 0]; t(n,m)=Coefficients(p(x,n)).
%e Triangle begins:
%e {1},
%e {1, 1},
%e {1, 1, 1},
%e {1, 2, 2, 1},
%e {1, 3, 4, 3, 1},
%e {1, 4, 8, 8, 4, 1},
%e {1, 5, 12, 16, 12, 5, 1},
%e {1, 6, 17, 28, 28, 17, 6, 1},
%e {1, 7, 23, 45, 56, 45, 23, 7, 1},
%e {1, 8, 30, 68, 101, 101, 68, 30, 8, 1},
%e {1, 9, 38, 98, 169, 202, 169, 98, 38, 9, 1},
%e {1, 10, 47, 136, 267, 371, 371, 267, 136, 47, 10, 1},
%e ...
%t p[x_, n_] = (x + 1)^n + If[n >= 2, x^2*(x + 1)^(n - 1), x^(n + 1)] + If[n >= 4, x^2*(x + 1)^(n - 3), 0]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]
%Y Cf. A072405, A259098.
%K nonn,tabl
%O 0,8
%A _Roger L. Bagula_, Nov 01 2008
%E Partially edited by _N. J. A. Sloane_, Jun 22 2015
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