A301986 - OEIS

%I #6 Mar 31 2018 04:52:43

%S 1,1,2,8,15,41,75,179,378,748,1591,3133,6369,12357,24225,46691,89301,

%T 169589,318413,596255,1103468,2036880,3725353,6786021,12281026,

%U 22107132,39604155,70566697,125209095,221048851,388705826,680465440,1186649341,2061086935

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

%H Vaclav Kotesovec, <a href="/A301986/b301986.txt">Table of n, a(n) for n = 0..10000</a>

%F 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)).

%t nmax = 40; CoefficientList[Series[Product[(1+x^k)^(k*EulerPhi[k]), {k, 1, nmax}], {x, 0, nmax}], x]

%t 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]

%Y Cf. A002618, A061255, A226106, A299069.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Mar 30 2018