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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
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, 1559, 98, 1, 1, 195, 6361, 40003, 40003, 6361, 195, 1, 1, 388, 25372, 345692, 862598, 345692, 25372, 388, 1, 1, 773, 100640, 2813688, 16569442, 16569442, 2813688 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

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

LINKS

Table of n, a(n) for n=0..51.

FORMULA

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];

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

EXAMPLE

{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, 1559, 98, 1},

{1, 195, 6361, 40003, 40003, 6361, 195, 1},

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

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

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

MATHEMATICA

Clear[p, n, m, x]; m = 0; 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: A146898 A152970 A154986 * A324916 A156534 A168287

Adjacent sequences:  A154980 A154981 A154982 * A154984 A154985 A154986

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 18 2009

STATUS

approved

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Last modified October 15 03:16 EDT 2019. Contains 328025 sequences. (Running on oeis4.)