A146772 - OEIS

%I #8 Apr 23 2019 09:18:00

%S 1,1,1,1,6,1,1,11,11,1,1,28,22,28,1,1,69,58,58,69,1,1,166,207,84,207,

%T 166,1,1,391,661,291,291,661,391,1,1,904,1948,1336,326,1336,1948,904,

%U 1,1,2057,5412,5204,1406,1406,5204,5412,2057,1,1,4618,14381,18040,7890

%N Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n-1)*Sum[Binomial[n-m, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].

%C Row sums are: {1, 2, 8, 24, 80, 256, 832, 2688, 8704, 28160, 91136}.

%e Triangle begins:

%e {1},

%e {1, 1},

%e {1, 6, 1},

%e {1, 11, 11, 1},

%e {1, 28, 22, 28, 1},

%e {1, 69, 58, 58, 69, 1},

%e {1, 166, 207, 84, 207, 166, 1},

%e {1, 391, 661, 291, 291, 661, 391, 1},

%e {1, 904, 1948, 1336, 326, 1336, 1948, 904, 1},

%e {1, 2057, 5412, 5204, 1406, 1406, 5204, 5412, 2057, 1},

%e {1, 4618, 14381, 18040, 7890, 1276, 7890, 18040, 14381, 4618, 1}

%t p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n-1)*Sum[Binomial[n-m, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]];

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

%K nonn,tabl,less

%O 0,5

%A _Roger L. Bagula_, Nov 02 2008