Voozh

A356346

a(n) = Sum_{k=1..n} binomial(2*k, k) * phi(k), where phi is the Euler totient function.

2, 8, 48, 188, 1196, 3044, 23636, 75116, 366836, 1105860, 8160180, 18976804, 143784004, 384483604, 1625423764, 6434066884, 43771766404, 98222578204, 734437326604, 1837209557164, 8296304050444, 29337293687644, 210472769694844, 468453599159644, 2996665727914684

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The average value of a(n) is sqrt(n) * 2^(2*n+3) / Pi^(5/2).

LINKS

Table of n, a(n) for n=1..25.

MATHEMATICA

Table[Sum[Binomial[2*k, k]*EulerPhi[k], {k, 1, n}], {n, 1, 30}]

PROG

(PARI) a(n) = sum(k=1, n, binomial(2*k, k) * eulerphi(k)); \\ Michel Marcus, Aug 05 2022

CROSSREFS