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A143505 Triangle of coefficients of the polynomials x^(n - 1)*A(n,x + 1/x), where A(n,x) are the Eulerian polynomials of A008292. 2
1, 1, 1, 1, 1, 4, 3, 4, 1, 1, 11, 14, 23, 14, 11, 1, 1, 26, 70, 104, 139, 104, 70, 26, 1, 1, 57, 307, 530, 973, 947, 973, 530, 307, 57, 1, 1, 120, 1197, 3016, 5970, 8568, 9549, 8568, 5970, 3016, 1197, 120, 1, 1, 247, 4300, 17101, 37105, 70474, 90069, 107241, 90069 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Row sums yield A000670 (without leading 1).

LINKS

Table of n, a(n) for n=1..58.

Eric Weisstein's World of Mathematics, Polylogarithm

FORMULA

Row n is generated by the polynomial (1 - x - 1/x)^(n + 1)*x^(n - 1)*Li(-n, x + 1/x)/(x + 1/x), where Li(n, z) is the polylogarithm function.

E.g.f.: (exp(x*y) - exp((1 + x^2)*y))/(x*exp((1 + x^2)*y) - (1 + x^2)*exp(x*y)). - Franck Maminirina Ramaharo, Oct 25 2018

EXAMPLE

Triangle begins:

   1;

   1,  1,   1;

   1,  4,   3,   4,   1;

   1, 11,  14,  23,  14,  11,   1;

   1, 26,  70, 104, 139, 104,  70,  26,   1;

   1, 57, 307, 530, 973, 947, 973, 530, 307, 57, 1;

    ... reformatted. - Franck Maminirina Ramaharo, Oct 25 2018

MATHEMATICA

Table[CoefficientList[FullSimplify[ExpandAll[(1 - x - 1/x)^(n + 1)*x^(n - 1)*PolyLog[-n, x + 1/x]/(x + 1/x)]], x], {n, 1, 10}]//Flatten

CROSSREFS

Compare with A141720.

Cf. A008292.

Cf. A143506, A143507.

Sequence in context: A070511 A066340 A195597 * A245727 A280822 A284517

Adjacent sequences:  A143502 A143503 A143504 * A143506 A143507 A143508

KEYWORD

nonn,tabf

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 25 2008

EXTENSIONS

Edited and new name by Franck Maminirina Ramaharo, Oct 25 2018

STATUS

approved

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Last modified December 18 12:06 EST 2018. Contains 318229 sequences. (Running on oeis4.)