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A146959 A functionally symmetric Polynomial as a triangle of coefficients: p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[(3^(m-1) + 2*m+(n-1) )*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]. 0
1, 1, 1, 1, 6, 1, 1, 17, 17, 1, 1, 52, 46, 52, 1, 1, 189, 130, 130, 189, 1, 1, 838, 431, 340, 431, 838, 1, 1, 4327, 1781, 1027, 1027, 1781, 4327, 1, 1, 24328, 8860, 3896, 2758, 3896, 8860, 24328, 1, 1, 142217, 49060, 18388, 9214, 9214, 18388, 49060, 142217, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:{1, 2, 8, 36, 152, 640, 2880, 14272, 76928, 437760, 2564096}.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[(3^(m-1) + 2*m+(n-1) )*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; t(n,m)=coefficients(p(x,n)).

EXAMPLE

{1}, {1, 1}, {1, 6, 1}, {1, 17, 17, 1}, {1, 52, 46, 52, 1}, {1, 189, 130, 130, 189, 1}, {1, 838, 431, 340, 431, 838, 1}, {1, 4327, 1781, 1027, 1027, 1781, 4327, 1}, {1, 24328, 8860, 3896, 2758, 3896, 8860, 24328, 1}, {1, 142217, 49060, 18388, 9214, 9214, 18388, 49060, 142217, 1}, {1, 844810, 285229, 99448, 39634, 25852, 39634, 99448, 285229, 844810, 1}

MATHEMATICA

Clear[p, x, n]; p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[(3^(m-1) + 2*m+(n-1) )*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]

CROSSREFS

Sequence in context: A154985 A157275 A157268 * A157632 A176125 A168289

Adjacent sequences:  A146956 A146957 A146958 * A146960 A146961 A146962

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Nov 03 2008

STATUS

approved

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Last modified May 26 22:57 EDT 2019. Contains 323597 sequences. (Running on oeis4.)