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A175353 Antidiagonal expansion of (x + x^(m + 1))/(1 - 2*x - x^(m + 1)).

%I A175353 #11 Dec 10 2016 17:32:26
%S A175353 2,6,1,18,3,1,54,7,2,1,162,17,5,2,1,486,41,11,4,2,1,1458,99,24,9,4,2,
%T A175353 1,4374,239,53,19,8,4,2,1,13122,577,117,40,17,8,4,2,1
%N A175353 Antidiagonal expansion of (x + x^(m + 1))/(1 - 2*x - x^(m + 1)).
%C A175353 Row sums are {0, 2, 7, 22, 64, 187, 545, 1597, 4700, 13888, ...};
%C A175353 I reversed the signs on Riordan's Fibonacci function.
%D A175353 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 125 and 155.
%F A175353 G.f.: f(x,m) = (x + x^(m + 1))/(1 - 2*x - x^(m + 1)).
%e A175353 {2},
%e A175353 {6, 1},
%e A175353 {18, 3, 1},
%e A175353 {54, 7, 2, 1},
%e A175353 {162, 17, 5, 2, 1},
%e A175353 {486, 41, 11, 4, 2, 1},
%e A175353 {1458, 99, 24, 9, 4, 2, 1},
%e A175353 {4374, 239, 53, 19, 8, 4, 2, 1},
%e A175353 {13122, 577, 117, 40, 17, 8, 4, 2, 1}
%t A175353 f[x_, n_] = (x + x^(m + 1))/(1 - 2*x - x^(m + 1));
%t A175353 a = Table[Table[SeriesCoefficient[
%t A175353       Series[f[x, m], {x, 0, 10}], n], {n, 0, 10}], {m, 0, 10}];
%t A175353 Table[Table[a[[m, n - m + 1]], {m, 1, n - 1}], {n, 1, 10}];
%t A175353 Flatten[%]
%Y A175353 Cf. A175331.
%K A175353 nonn,tabl
%O A175353 0,1
%A A175353 _Roger L. Bagula_, Dec 03 2010