A356340 a(n) = Sum_{k=1..n} binomial(2*n, n-k) * phi(k), where phi is the Euler totient function.

1, 5, 23, 102, 444, 1909, 8133, 34404, 144714, 605920, 2527348, 10507978, 43569096, 180219699, 743907057, 3065019864, 12607648238, 51783970314, 212412697368, 870249992168, 3561502879100, 14560944187796, 59476980459794, 242741090637012, 989921853052930, 4034101567907172

Offset: 1

Author

Vaclav Kotesovec, Aug 04 2022

Keywords

• nonn

Crossrefs

Cf. A000010, A002088, A306988, A351146.

Programs

Mathematica

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

PARI

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

Formula

a(n) ~ 3 * sqrt(n) * 4^n / Pi^(5/2).