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 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). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row sums are:A014479 0, 1, 8, 72, 768, 9600, 138240, 2257920, 41287680, 836075520, 18579456000. LINKS 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)). EXAMPLE {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} 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[%] CROSSREFS Cf. A060187, A014479. Sequence in context: A201445 A090033 A036173 * A305874 A176965 A084249 Adjacent sequences:  A142704 A142705 A142706 * A142708 A142709 A142710 KEYWORD nonn,uned AUTHOR Roger L. Bagula and Gary W. Adamson, Sep 24 2008 STATUS approved

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Last modified January 17 15:12 EST 2020. Contains 330958 sequences. (Running on oeis4.)