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 A303361 Expansion of Product_{n>=1} ((1 + (4*x)^n)/(1 - (4*x)^n))^(1/4). 6

%I

%S 1,2,10,60,262,1372,7044,32760,153670,789676,3659820,17109320,

%T 83073180,381273240,1786996424,8604391920,38832248902,179714213580,

%U 845485079580,3834271942440,17666638985652,81920437065288,370224975781560,1685489994025360

%N Expansion of Product_{n>=1} ((1 + (4*x)^n)/(1 - (4*x)^n))^(1/4).

%H Seiichi Manyama, <a href="/A303361/b303361.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ 2^(2*n - 5/2) * exp(sqrt(n)*Pi/2) / n^(13/16). - _Vaclav Kotesovec_, Apr 23 2018

%p seq(coeff(series(mul(((1+(4*x)^k)/(1-(4*x)^k))^(1/4), k = 1..n), x, n+1), x, n), n = 0..35); # _Muniru A Asiru_, Apr 22 2018

%t nmax = 30; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^(1/4), {k, 1, nmax}], {x, 0, nmax}], x] * 4^Range[0, nmax] (* _Vaclav Kotesovec_, Apr 23 2018 *)

%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1+(4*x)^k)/(1-(4*x)^k))^(1/4)))

%Y Expansion of Product_{n>=1} ((1 + (2^b*x)^n)/(1 - (2^b)*x^n))^(1/(2^b)): A015128 (b=0), A303307 (b=1), this sequence (b=2).

%Y Cf. A303360.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 22 2018

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Last modified January 19 15:20 EST 2021. Contains 340270 sequences. (Running on oeis4.)