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

1,1

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

Cf. A000010, A002088, A306988.

Sequence in context: A193944 A058928 A228288 * A292277 A173841 A004141

Adjacent sequences: A356343 A356344 A356345 * A356347 A356348 A356349

Keyword

nonn

Author

Vaclav Kotesovec, Aug 04 2022

Status

approved