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A303361 Expansion of Product_{n>=1} ((1 + (4*x)^n)/(1 - (4*x)^n))^(1/4). 6
1, 2, 10, 60, 262, 1372, 7044, 32760, 153670, 789676, 3659820, 17109320, 83073180, 381273240, 1786996424, 8604391920, 38832248902, 179714213580, 845485079580, 3834271942440, 17666638985652, 81920437065288, 370224975781560, 1685489994025360 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ 2^(2*n - 5/2) * exp(sqrt(n)*Pi/2) / n^(13/16). - Vaclav Kotesovec, Apr 23 2018

MAPLE

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

MATHEMATICA

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 *)

PROG

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

CROSSREFS

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).

Cf. A303360.

Sequence in context: A095993 A029725 A246480 * A026161 A025188 A114620

Adjacent sequences:  A303358 A303359 A303360 * A303362 A303363 A303364

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Apr 22 2018

STATUS

approved

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Last modified March 6 20:37 EST 2021. Contains 341850 sequences. (Running on oeis4.)