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

Offset: 1

Author

Vaclav Kotesovec, Aug 04 2022

Keywords

• nonn

Comments

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

Crossrefs

Cf. A000010, A002088, A306988.

Programs

Mathematica

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

PARI

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