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A328128 G.f.: K(4*sqrt(x)) / E(4*sqrt(x)), where E(), K() are complete elliptic integrals. 2

%I #7 Oct 05 2019 08:32:59

%S 1,8,80,896,10784,136448,1790720,24160256,333053504,4670325248,

%T 66403043840,954931245056,13863783325184,202898094829568,

%U 2989879597076480,44320135356317696,660370844304147584,9884176356444627968,148535796374189204480,2240105752104228970496

%N G.f.: K(4*sqrt(x)) / E(4*sqrt(x)), where E(), K() are complete elliptic integrals.

%C Convolution of A002894 and A188266.

%H Vaclav Kotesovec, <a href="/A328128/b328128.txt">Table of n, a(n) for n = 0..820</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/CompleteEllipticIntegraloftheFirstKind.html">Complete Elliptic Integral of the First Kind</a>.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/CompleteEllipticIntegraloftheSecondKind.html">Complete Elliptic Integral of the Second Kind</a>.

%F a(n) ~ 2^(4*n-1) / n.

%p seq(coeff(series(EllipticK(4*sqrt(x))/EllipticE(4*sqrt(x)), x, 21), x, n), n = 0..20);

%t CoefficientList[Series[EllipticK[16*x]/EllipticE[16*x], {x, 0, 20}], x]

%Y Cf. A002894, A188266, A261976, A328127.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Oct 04 2019

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Last modified April 25 07:53 EDT 2024. Contains 371964 sequences. (Running on oeis4.)