%I #17 Oct 27 2018 02:52:20
%S 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,
%T 237,1687,2630,5293,4787,5293,2630,1687,237,1,1,722,10549,27158,52730,
%U 78586,84365,78586,52730,27158,10549,722,1,1,2179,60664,272797,563029,1132234
%N 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.
%C Row sums yield A080253.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lerch_zeta_function">Lerch zeta function</a>
%F 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.
%F 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
%e Triangle begins:
%e 1;
%e 1, 1, 1;
%e 1, 6, 3, 6, 1;
%e 1, 23, 26, 47, 26, 23, 1;
%e 1, 76, 234, 304, 467, 304, 234, 76, 1;
%e 1, 237, 1687, 2630, 5293, 4787, 5293, 2630, 1687, 237, 1;
%e ... reformatted. - _Franck Maminirina Ramaharo_, Oct 25 2018
%t 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
%Y Cf. A008292, A060187.
%Y Cf. A143505, A143507.
%K nonn,tabf
%O 0,6
%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 25 2008
%E Edited, new name, and offset corrected by _Franck Maminirina Ramaharo_, Oct 25 2018