A142707 - OEIS

%I #2 Oct 12 2012 14:54:52

%S 1,6,2,23,46,3,76,460,228,4,237,3364,5046,948,5,722,21086,70644,42172,

%T 3610,6,2179,121314,779169,1038892,303285,13074,7,6552,663224,7455864,

%U 18700056,12426440,1989672,45864,8,19673,3512680,65123916,277653176

%N 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).

%C Row sums are:A014479

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

%F 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)).

%e {1},

%e {6, 2},

%e {23, 46, 3},

%e {76, 460, 228, 4},

%e {237, 3364, 5046, 948, 5},

%e {722, 21086, 70644, 42172, 3610, 6},

%e {2179, 121314, 779169, 1038892, 303285, 13074, 7},

%e {6552, 663224, 7455864, 18700056, 12426440, 1989672, 45864, 8},

%e {19673, 3512680, 65123916, 277653176, 347066470, 130247832, 12294380, 157384, 9},

%e {59038, 18232282, 534902712, 3627693128, 7635462340, 5441539692, 1248106328, 72929128, 531342, 10}

%t 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[%]

%Y Cf. A060187, A014479.

%K nonn,uned

%O 1,2

%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 24 2008