A301986 Expansion of Product_{k>=1} (1 + x^k)^(k*A000010(k)), where A000010 is the Euler totient function.

1, 1, 2, 8, 15, 41, 75, 179, 378, 748, 1591, 3133, 6369, 12357, 24225, 46691, 89301, 169589, 318413, 596255, 1103468, 2036880, 3725353, 6786021, 12281026, 22107132, 39604155, 70566697, 125209095, 221048851, 388705826, 680465440, 1186649341, 2061086935

Offset: 0

Author

Vaclav Kotesovec, Mar 30 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A002618, A061255, A226106, A299069.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[(1+x^k)^(k*EulerPhi[k]), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 40; CoefficientList[Series[Exp[Sum[(-1)^(j + 1)/j * Sum[k*EulerPhi[k] * x^(j*k), {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x]

Formula

a(n) ~ exp(2^(3/2) * 7^(1/4) * sqrt(Pi) * n^(3/4) / (3 * 5^(1/4))) * 7^(1/8) / (2^(7/4) * 5^(1/8) * Pi^(1/4) * n^(5/8)).