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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
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
1,2
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 04 2022
STATUS
approved