Dear David
That above in Mathematica notation works, but not this (similar also in Mathematica notation):
Sum[(CatalanNumber[k]/2^(2 k + 1))^2 (17 k + 19), {k, 0, Infinity}]
Input interpretation:
sum(k=0)^infinity (Ck/2^(2 k+1))^2 (17 k+19)
Convergence tests:
The ratio test is inconclusive.
By the comparison test, the series converges.
Partial sum formula:
sum(k=0)^n (Ck/2^(2 k+1))^2 (17 k+19) = (25 n^3 Gamma(1/2 (2 n+3))^2+127 n^2 Gamma(1/2 (2 n+3))^2+208 n Gamma(1/2 (2 n+3))^2-2 pi Gamma(n+3)^2+108 Gamma(1/2 (2 n+3))^2)/(pi Gamma(n+3)^2)
