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A330148
a(n) = Sum_{k=1..n} binomial(n,k) * phi(k) * phi(n - k + 1), where phi = A000010.
0
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
1,2
FORMULA
E.g.f.: (1/2) * d/dx (Sum_{k>=1} phi(k) * x^k / k!)^2.
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
PROG
(Magma) [&+[Binomial(n, k)*EulerPhi(k)*EulerPhi(n-k+1):k in [1..n]]:n in [1..30]]; // Marius A. Burtea, Dec 03 2019
(PARI) a(n) = sum(k=1, n, binomial(n, k)*eulerphi(k)*eulerphi(n-k+1)); \\ Michel Marcus, Dec 03 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 03 2019
STATUS
approved