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

0,3

Links

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

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)).

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]

Crossrefs

Cf. A002618, A061255, A226106, A299069.

Sequence in context: A305674 A082638 A077388 * A296798 A203419 A173287

Adjacent sequences: A301983 A301984 A301985 * A301987 A301988 A301989

Keyword

nonn

Author

Vaclav Kotesovec, Mar 30 2018

Status

approved