A146568 Coefficients of Pascal's triangle polynomial minus MacMahon polynomial A060187 with a power of x divided out: q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((x+1)^n-q(x,n))/x.

4, 20, 20, 72, 224, 72, 232, 1672, 1672, 232, 716, 10528, 23528, 10528, 716, 2172, 60636, 259688, 259688, 60636, 2172, 6544, 331584, 2485232, 4674944, 2485232, 331584, 6544, 19664, 1756304, 21707888, 69413168, 69413168, 21707888, 1756304

Offset: 2

Author

Roger L. Bagula, Nov 01 2008

Keywords

• nonn
• tabl
• uned
• less

Comments

First elements in each row are: 3^n - 2*n - 1 (A061981).

Examples

			Triangle starts:
{4},
{20, 20},
{72, 224, 72},
{232, 1672, 1672, 232},
{716, 10528, 23528, 10528, 716},
{2172, 60636, 259688, 259688, 60636, 2172},
{6544, 331584, 2485232, 4674944, 2485232, 331584, 6544},
{19664, 1756304, 21707888, 69413168, 69413168, 21707888, 1756304, 19664},
{59028, 9116096, 178300784, 906923072, 1527092216, 906923072, 178300784, 9116096, 59028}
		

Crossrefs

Cf. A061981, A060187.

Programs

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; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 2, 10}]; Flatten[%]

Formula

q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((x+1)^n-q(x,n))/x; t(n,m)=Coefficients(p(x,n)) with n starting at 2.