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A154985 Polynomial recursion:m=1; 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
1, 1, 1, 1, 6, 1, 1, 17, 17, 1, 1, 38, 154, 38, 1, 1, 79, 872, 872, 79, 1, 1, 160, 3991, 14064, 3991, 160, 1, 1, 321, 16791, 157575, 157575, 16791, 321, 1, 1, 642, 68312, 1451486, 4815630, 1451486, 68312, 642, 1, 1, 1283, 274394, 12266038, 107115116, 107115116 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 8, 36, 232, 1904, 22368, 349376, 7856512, 239313664, 10534962688,...}.

LINKS

Table of n, a(n) for n=0..50.

FORMULA

m=1; 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];

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

EXAMPLE

{1},

{1, 1},

{1, 6, 1},

{1, 17, 17, 1},

{1, 38, 154, 38, 1},

{1, 79, 872, 872, 79, 1},

{1, 160, 3991, 14064, 3991, 160, 1},

{1, 321, 16791, 157575, 157575, 16791, 321, 1},

{1, 642, 68312, 1451486, 4815630, 1451486, 68312, 642, 1},

{1, 1283, 274394, 12266038, 107115116, 107115116, 12266038, 274394, 1283, 1},

{1, 2564, 1097437, 99979792, 1977283234, 6378236632, 1977283234, 99979792, 1097437, 2564, 1}

MATHEMATICA

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

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];

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

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

Flatten[%]

CROSSREFS

Sequence in context: A152602 A119726 A103999 * A157275 A157268 A146959

Adjacent sequences:  A154982 A154983 A154984 * A154986 A154987 A154988

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 18 2009

STATUS

approved

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Last modified April 20 09:59 EDT 2019. Contains 322309 sequences. (Running on oeis4.)