A174802 - OEIS

%I #4 Dec 10 2016 17:31:19

%S 1,1,1,1,2,1,1,3,3,1,1,5,5,4,1,1,8,9,8,5,1,1,13,17,14,12,6,1,1,21,31,

%T 27,22,17,7,1,1,34,57,53,41,34,23,8,1

%N Triangular sequence from antidiagonal expansion of: p(x,m) = x*(x + 1)^(m - 1)/(1 - Sum[x^i, {i, 1, m}]).

%C Row sums are {1, 2, 4, 8, 16, 32, 64, 127, 252, ...}.

%F p(x,m) = x*(x + 1)^(m - 1)/(1 - Sum[x^i, {i, 1, m}]);

%F t(n,m) = antidiagonal(expansion(p,x,n))).

%e {1},

%e {1, 1},

%e {1, 2, 1},

%e {1, 3, 3, 1},

%e {1, 5, 5, 4, 1},

%e {1, 8, 9, 8, 5, 1},

%e {1, 13, 17, 14, 12, 6, 1},

%e {1, 21, 31, 27, 22, 17, 7, 1},

%e {1, 34, 57, 53, 41, 34, 23, 8, 1}

%t p[x_, m_] = x*(x + 1)^(m - 1)/(1 - Sum[x^i, {i, 1, m}])

%t a = Table[Table[SeriesCoefficient[Series[FullSimplify[ExpandAll[ p[x, m]]], {x, 0, 50}], n], {n, 0, 10}], {m, 1, 10}]

%t Table[Table[a[[m, n - m + 1]], {m, 1, n - 1}], {n, 2, 10}]

%t Flatten[%]

%t Table[Sum[a[[m, n - m + 1]], {m, 1, n - 1}], {n, 2, 10}]

%K nonn,tabl,uned

%O 1,5

%A _Roger L. Bagula_, Mar 29 2010