|
| |
|
|
A146745
|
|
Coefficients of Pascals triangle polynomial minus MacMahon polynomial A060187 with minus the first and last row terms and powers of x divided out: f(n)=3^n - 2*n - 1; q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((q[x, n] - (x + 1)^n)/x - f[n] - f[n]*x^(n - 2))/x.
|
|
0
| |
|
|
224, 1672, 1672, 10528, 23528, 10528, 60636, 259688, 259688, 60636, 331584, 2485232, 4674944, 2485232, 331584, 1756304, 21707888, 69413168, 69413168, 21707888, 1756304, 9116096, 178300784, 906923072, 1527092216, 906923072
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 2,1
|
|
|
COMMENTS
| Row sums starting with n=4 are:{224, 3344, 44584, 640648, 10308576, 185754720, 3715772120}. First elements in each row are:{224, 1672, 1672, 10528, 60636, 331584, 1756304, 9116096}. Subtracting out the row terms gives the middle elements of the difference.
|
|
|
FORMULA
| f(n)=3^n - 2*n - 1; q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((q[x, n] - (x + 1)^n)/x - f[n] - f[n]*x^(n - 2))/x; t(n,m)=Coefficients(p(x,n)) with n starting at 4.
|
|
|
EXAMPLE
| {224}, {1672, 1672}, {10528, 23528, 10528}, {60636, 259688, 259688, 60636}, {331584, 2485232, 4674944, 2485232, 331584}, {1756304, 21707888, 69413168, 69413168, 21707888, 1756304}, {9116096, 178300784, 906923072, 1527092216, 906923072, 178300784, 9116096}
|
|
|
MATHEMATICA
| q[x_, n_] = 2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p[x_, n_] = ((q[x, n] - (x + 1)^n)/x - f[n] - f[n]*x^(n - 2))/x; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 4, 10}]; Flatten[%]
|
|
|
CROSSREFS
| A061981, A060187
Sequence in context: A158227 A061524 A156813 * A015048 A032802 A007771
Adjacent sequences: A146742 A146743 A146744 * A146746 A146747 A146748
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 01 2008
|
| |
|
|
