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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

Table of n, a(n) for n=1..40.

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.)