Subtraction of polynomial coefficients of MacMahon A060187 from third derivative of Pascal's triangle A155863: p(x,n)=(If[n == 0, 1, x^n + 1 + x*D[( x + 1)^(n + 1), {x, 3}]] - 2^n*(1 - x)^(1 + n)*LerchPhi[x, -n, 1/2])/x.

A155871

Subtraction of polynomial coefficients of MacMahon A060187 from third derivative of Pascal's triangle A155863: p(x,n)=(If[n == 0, 1, x^n + 1 + x*D[( x + 1)^(n + 1), {x, 3}]] - 2^n*(1 - x)^(1 + n)*LerchPhi[x, -n, 1/2])/x.