A triangle of polynomial coefficients: q(x,n)=(-1)^(n + 1)*(x - 1)^(3*n + 1)*Sum[(Binomial[m, n]* Binomial[m + 1, n + 1]/(m - n + 1))*(2*m + 1)^n*x^ m, {m, 0, Infinity}]/(x^n); p(x,n)=q(x,n)+x^n*q(1/x,n).

A155948

A triangle of polynomial coefficients: q(x,n)=(-1)^(n + 1)*(x - 1)^(3*n + 1)*Sum[(Binomial[m, n]* Binomial[m + 1, n + 1]/(m - n + 1))*(2*m + 1)^n*x^ m, {m, 0, Infinity}]/(x^n); p(x,n)=q(x,n)+x^n*q(1/x,n).