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A154989 Symmetrical triangle sequence from polynomials: q(x,n)=(-1)^n*(Sum[(k + 1)^n*x^k/k, {k, 1, Infinity}] + Log[1 - x])*(x - 1)^n/x; p(x,n)=q(x,n)+x^n*q(1/x,n). 0
2, 1, 1, 10, -16, 10, 11, -5, -5, 11, 36, -58, 92, -58, 36, 57, 21, 42, 42, 21, 57, 134, 156, 618, -376, 618, 156, 134, 247, 1303, 2529, 961, 961, 2529, 1303, 247, 520, 5162, 17524, 12646, 8936, 12646, 17524, 5162, 520, 1013, 19393, 99880, 153472, 89122 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row sums are: 2*n!;

{2, 2, 4, 12, 48, 240, 1440, 10080, 80640, 725760,...}

LINKS

Table of n, a(n) for n=1..50.

FORMULA

q(x,n)=(-1)^n*(Sum[(k + 1)^n*x^k/k, {k, 1, Infinity}] + Log[1 - x])*(x - 1)^n/x;

p(x,n)=q(x,n)+x^n*q(1/x,n);

t(n,m)=coefficients(p(x,n)).

EXAMPLE

{2},

{1, 1},

{10, -16, 10},

{11, -5, -5, 11},

{36, -58, 92, -58, 36},

{57, 21, 42, 42, 21, 57},

{134, 156, 618, -376, 618, 156, 134},

{247, 1303, 2529, 961, 961, 2529, 1303, 247},

{520, 5162, 17524, 12646, 8936, 12646, 17524, 5162, 520},

{1013, 19393, 99880, 153472, 89122, 89122, 153472, 99880, 19393, 1013}

MATHEMATICA

Clear[p, x, n];

p[x_, n_] = (-1)^n*(Sum[(k + 1)^n*x^k/k, {k, 1, Infinity}] + Log[1 - x])*(x - 1)^n/x;

Table[FullSimplify[ExpandAll[p[x, n]]], {n, 1, 10}];

Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x] + Reverse[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]], {n, 1, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A153731 A262226 A298158 * A064307 A165883 A260950

Adjacent sequences:  A154986 A154987 A154988 * A154990 A154991 A154992

KEYWORD

uned,sign

AUTHOR

Roger L. Bagula, Jan 18 2009

STATUS

approved

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Last modified December 12 19:15 EST 2018. Contains 318081 sequences. (Running on oeis4.)