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A154984 Polynomial recursion:m=2; 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, 10, 1, 1, 29, 29, 1, 1, 66, 418, 66, 1, 1, 139, 2572, 2572, 139, 1, 1, 284, 12215, 65336, 12215, 284, 1, 1, 573, 52531, 818287, 818287, 52531, 573, 1, 1, 1150, 216688, 7906658, 39270110, 7906658, 216688, 1150, 1, 1, 2303, 877934, 68639058 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 12, 60, 552, 5424, 90336, 1742784, 55519104, 2118725376, 132153466368,...}.

LINKS

Table of n, a(n) for n=0..48.

FORMULA

m=2; 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, 10, 1},

{1, 29, 29, 1},

{1, 66, 418, 66, 1},

{1, 139, 2572, 2572, 139, 1},

{1, 284, 12215, 65336, 12215, 284, 1},

{1, 573, 52531, 818287, 818287, 52531, 573, 1},

{1, 1150, 216688, 7906658, 39270110, 7906658, 216688, 1150, 1},

{1, 2303, 877934, 68639058, 989843392, 989843392, 68639058, 877934, 2303, 1},

{1, 4608, 3529837, 568766144, 19275422482, 92458020224, 19275422482, 568766144, 3529837, 4608, 1}

MATHEMATICA

Clear[p, n, m, x]; m = 2; 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: A154979 A146765 A190152 * A173047 A173045 A176491

Adjacent sequences:  A154981 A154982 A154983 * A154985 A154986 A154987

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 18 2009

STATUS

approved

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Last modified August 5 05:22 EDT 2020. Contains 336209 sequences. (Running on oeis4.)