A146958 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+1 )*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].

1, 1, 1, 1, 6, 1, 1, 15, 15, 1, 1, 44, 38, 44, 1, 1, 165, 106, 106, 165, 1, 1, 774, 367, 276, 367, 774, 1, 1, 4167, 1621, 867, 867, 1621, 4167, 1, 1, 23944, 8476, 3512, 2374, 3512, 8476, 23944, 1, 1, 141321, 48164, 17492, 8318, 8318, 17492, 48164, 141321, 1, 1

Offset

0,5

Comments

Row sums are:{1, 2, 8, 32, 128, 544, 2560, 13312, 74240, 430592, 2545664}.

Links

Table of n, a(n) for n=0..55.

Formula

p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[(3^(m-1) + 2*m+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, 15, 15, 1}, {1, 44, 38, 44, 1}, {1, 165, 106, 106, 165, 1}, {1, 774, 367, 276, 367, 774, 1}, {1, 4167, 1621, 867, 867, 1621, 4167, 1}, {1, 23944, 8476, 3512, 2374, 3512, 8476, 23944, 1}, {1, 141321, 48164, 17492, 8318, 8318, 17492, 48164, 141321, 1}, {1, 842762, 283181, 97400, 37586, 23804, 37586, 97400, 283181, 842762, 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+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: A166344 A146766 A176152 * A154653 A376730 A109001

Adjacent sequences: A146955 A146956 A146957 * A146959 A146960 A146961

Keyword

nonn

Author

Roger L. Bagula, Nov 03 2008

Status

approved