A142707 Coefficients of derivatives of MacMahon polynomials (A060187): p(x,n)=2^n*(1 - x)^(1 + n)*LerchPhi[x, -n, 1/2]; p'(x,n)=(d/dx)p{x,n).

1, 6, 2, 23, 46, 3, 76, 460, 228, 4, 237, 3364, 5046, 948, 5, 722, 21086, 70644, 42172, 3610, 6, 2179, 121314, 779169, 1038892, 303285, 13074, 7, 6552, 663224, 7455864, 18700056, 12426440, 1989672, 45864, 8, 19673, 3512680, 65123916, 277653176

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Sep 24 2008

Keywords

• nonn
• uned

Comments

Row sums are:A014479

0, 1, 8, 72, 768, 9600, 138240, 2257920, 41287680, 836075520, 18579456000.

Examples

			{1},
{6, 2},
{23, 46, 3},
{76, 460, 228, 4},
{237, 3364, 5046, 948, 5},
{722, 21086, 70644, 42172, 3610, 6},
{2179, 121314, 779169, 1038892, 303285, 13074, 7},
{6552, 663224, 7455864, 18700056, 12426440, 1989672, 45864, 8},
{19673, 3512680, 65123916, 277653176, 347066470, 130247832, 12294380, 157384, 9},
{59038, 18232282, 534902712, 3627693128, 7635462340, 5441539692, 1248106328, 72929128, 531342, 10}
		

Crossrefs

Cf. A060187, A014479.

Programs

Mathematica

Clear[p, x, n, a]; p[x_, n_] = 2^n*(1 - x)^(1 + n)*LerchPhi[x, -n, 1/2]; Table[FullSimplify[Expand[D[p[x, n], x]]], {n, 0, 10}]; Table[CoefficientList[FullSimplify[Expand[D[p[x, n], x]]], x], {n, 0, 10}]; Flatten[%]

Formula

p(x,n)=2^n*(1 - x)^(1 + n)*LerchPhi[x, -n, 1/2]; p'(x,n)=(d/dx)p{x,n); t(n,m)=Coefficients(p'(x,n)).