A330148 a(n) = Sum_{k=1..n} binomial(n,k) * phi(k) * phi(n - k + 1), where phi = A000010.

1, 3, 11, 30, 94, 238, 692, 1596, 4536, 9350, 27840, 52884, 149668, 294838, 782432, 1463224, 4095792, 7460274, 20229356, 36847380, 100317284, 170262974, 492659240, 814679680, 2184447760, 3965791284, 9988168320, 17883230712, 49362800340, 80674575956, 213420581248

Offset: 1

Author

Ilya Gutkovskiy, Dec 03 2019

Keywords

• nonn

Crossrefs

Cf. A000010, A007318, A065093, A306988.

Programs

Magma

[&+[Binomial(n,k)*EulerPhi(k)*EulerPhi(n-k+1):k in [1..n]]:n in [1..30]]; // Marius A. Burtea, Dec 03 2019

Mathematica

Table[Sum[Binomial[n, k] EulerPhi[k] EulerPhi[n - k + 1], {k, 1, n}], {n, 1, 31}]
nmax = 31; CoefficientList[Series[(1/2) D[Sum[EulerPhi[k] x^k/k!, {k, 1, nmax}]^2, x], {x, 0, nmax}], x] Range[0, nmax]! // Rest

PARI

a(n) = sum(k=1, n, binomial(n,k)*eulerphi(k)*eulerphi(n-k+1)); \\ Michel Marcus, Dec 03 2019

Formula

E.g.f.: (1/2) * d/dx (Sum_{k>=1} phi(k) * x^k / k!)^2.