A143506 Irregular triangle read by rows: first row is 1, and n-th row gives the coefficients of x^(n - 1)*R(n,x + 1/x)/(x + 1/x), where R(n,x) is the n-th row polynomial for A060187.

1, 1, 1, 1, 1, 6, 3, 6, 1, 1, 23, 26, 47, 26, 23, 1, 1, 76, 234, 304, 467, 304, 234, 76, 1, 1, 237, 1687, 2630, 5293, 4787, 5293, 2630, 1687, 237, 1, 1, 722, 10549, 27158, 52730, 78586, 84365, 78586, 52730, 27158, 10549, 722, 1, 1, 2179, 60664, 272797, 563029, 1132234

Offset

0,6

Comments

Row sums yield A080253.

Links

Table of n, a(n) for n=0..54.

Wikipedia, Lerch zeta function

Formula

Row n is generated by the polynomial 2^n*(1 - x - 1/x)^(1 + n)*x^n*Phi(x + 1/x, -n, 1/2), where Phi is the Lerch transcendant.

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

Example

Triangle begins:
   1;
   1,   1,    1;
   1,   6,    3,    6,    1;
   1,  23,   26,   47,   26,   23,    1;
   1,  76,  234,  304,  467,  304,  234,   76,    1;
   1, 237, 1687, 2630, 5293, 4787, 5293, 2630, 1687, 237, 1;
    ... reformatted. - Franck Maminirina Ramaharo, Oct 25 2018

Mathematica

Table[CoefficientList[FullSimplify[ExpandAll[2^n*(1 - x - 1/x)^(1 + n)*x^n*LerchPhi[x + 1/x, -n, 1/2]]], x], {n, 0, 10}]//Flatten

Crossrefs

Cf. A008292, A060187.

Cf. A143505, A143507.

Sequence in context: A241786 A019151 A367976 * A248580 A008567 A233700

Adjacent sequences: A143503 A143504 A143505 * A143507 A143508 A143509

Keyword

nonn,tabf

Author

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

Extensions

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

Status

approved