login
A146957
A functionally symmetric Polynomial as a triangle of coefficients: p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 2)*Sum[(3^(m-1) + 2*m-1 )*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].
0
1, 1, 1, 1, 6, 1, 1, 19, 19, 1, 1, 68, 54, 68, 1, 1, 293, 170, 170, 293, 1, 1, 1478, 655, 468, 655, 1478, 1, 1, 8199, 3093, 1571, 1571, 3093, 8199, 1, 1, 47624, 16668, 6712, 4422, 6712, 16668, 47624, 1, 1, 282121, 95780, 34388, 15998, 15998, 34388, 95780, 282121
OFFSET
0,5
COMMENTS
Row sums are:{1, 2, 8, 40, 192, 928, 4736, 25728, 146432, 856576, 5081088}.
FORMULA
p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 2)*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, 19, 19, 1}, {1, 68, 54, 68, 1}, {1, 293, 170, 170, 293, 1}, {1, 1478, 655, 468, 655, 1478, 1}, {1, 8199, 3093, 1571, 1571, 3093, 8199, 1}, {1, 47624, 16668, 6712, 4422, 6712, 16668, 47624, 1}, {1, 282121, 95780, 34388, 15998, 15998, 34388, 95780, 282121, 1}, {1, 1684490, 565293, 193656, 73938, 46332, 73938, 193656, 565293, 1684490, 1}
MATHEMATICA
Clear[p, x, n]; p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n - 2)*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: A168289 A141690 A318408 * A146988 A203954 A060972
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Nov 03 2008
STATUS
approved