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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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..26.

FORMULA

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

MATHEMATICA

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

PROG

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

CROSSREFS