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A146773 Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n)*Sum[Binomial[n-m, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]. 0

%I

%S 1,1,1,1,10,1,1,19,19,1,1,52,38,52,1,1,133,106,106,133,1,1,326,399,

%T 148,399,326,1,1,775,1301,547,547,1301,775,1,1,1800,3868,2616,582,

%U 2616,3868,1800,1,1,4105,10788,10324,2686,2686,10324,10788,4105,1,1,9226,28717

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

%C Row sums are: {1, 2, 12, 40, 144, 480, 1600, 5248, 17152, 55808, 181248}.

%e Triangle begins:

%e {1},

%e {1, 1},

%e {1, 10, 1},

%e {1, 19, 19, 1},

%e {1, 52, 38, 52, 1},

%e {1, 133, 106, 106, 133, 1},

%e {1, 326, 399, 148, 399, 326, 1},

%e {1, 775, 1301, 547, 547, 1301, 775, 1},

%e {1, 1800, 3868, 2616, 582, 2616, 3868, 1800, 1},

%e {1, 4105, 10788, 10324, 2686, 2686, 10324, 10788, 4105, 1},

%e {1, 9226, 28717, 35960, 15570, 2300, 15570, 35960, 28717, 9226, 1}

%t p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n)*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

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Last modified May 22 02:18 EDT 2022. Contains 353933 sequences. (Running on oeis4.)