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 A154983 Polynomial recursion:m=0; p(x,n)=(x + 1)*p(x, n - 1) + 2^(m + n - 1)*x*p(x, n - 2)+If[n >= 3, 2^(n - 2)*x*p(x, n - 2), 0]. 0

%I

%S 1,1,1,1,4,1,1,11,11,1,1,24,70,24,1,1,49,358,358,49,1,1,98,1559,4076,

%T 1559,98,1,1,195,6361,40003,40003,6361,195,1,1,388,25372,345692,

%U 862598,345692,25372,388,1,1,773,100640,2813688,16569442,16569442,2813688

%N Polynomial recursion:m=0; p(x,n)=(x + 1)*p(x, n - 1) + 2^(m + n - 1)*x*p(x, n - 2)+If[n >= 3, 2^(n - 2)*x*p(x, n - 2), 0].

%C Row sums are:

%C {1, 2, 6, 24, 120, 816, 7392, 93120, 1605504, 38969088, 1310965248,...}.

%F m=0; p(x,n)=(x + 1)*p(x, n - 1) + 2^(m + n - 1)*x*p(x, n - 2)

%F +If[n >= 3, 2^(n - 2)*x*p(x, n - 2), 0];

%F t(n,m)=coefficients(p(x,n))

%e {1},

%e {1, 1},

%e {1, 4, 1},

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

%e {1, 24, 70, 24, 1},

%e {1, 49, 358, 358, 49, 1},

%e {1, 98, 1559, 4076, 1559, 98, 1},

%e {1, 195, 6361, 40003, 40003, 6361, 195, 1},

%e {1, 388, 25372, 345692, 862598, 345692, 25372, 388, 1},

%e {1, 773, 100640, 2813688, 16569442, 16569442, 2813688, 100640, 773, 1},

%e {1, 1542, 399397, 22400024, 284874586, 695614148, 284874586, 22400024, 399397, 1542, 1}

%t Clear[p, n, m, x]; m = 0; p[x, 0] = 1; p[x, 1] = x + 1;

%t p[x, n] = (x + 1)*p[ x, n - 1] + 2^(m + n - 1)*x*p[x, n - 2]

%t + If[n >= 3, 2^(n - 2)*x*p[x, n - 2], 0];

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

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

%t Flatten[%]

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Jan 18 2009

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Last modified April 23 07:51 EDT 2019. Contains 322381 sequences. (Running on oeis4.)