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%I #21 Aug 03 2023 03:44:12
%S 2,8,128,512,32768,131072,2097152,8388608,2147483648,8589934592,
%T 137438953472,549755813888,35184372088832,140737488355328,
%U 2251799813685248,9007199254740992,9223372036854775808,36893488147419103232,590295810358705651712,2361183241434822606848
%N Denominator of coefficients of both EllipticK/Pi and EllipticE/Pi.
%C Denominators are powers of 2 since EllipticK(x) = Pi * Sum_{n>=0} 2^(-4*n-1) * binomial(2*n,n)^2 * x^n and EllipticE(x) = Pi * Sum_{n>=0} 2^(-4*n-1) (-1)^(2*n) * binomial(2*n,n)^2 /(-2*n+1) * x^n.
%H David P. Roberts and Fernando Rodriguez Villegas, <a href="https://doi.org/10.1090/noti2491">Hypergeometric Motives</a>, Notices of the American Mathematical Society, Vol. 69, No. 6 (2022), pp. 914-929; <a href="https://arxiv.org/abs/2109.00027">arXiv preprint</a>, arXiv:2109.00027 [math.AG], 2021. See eq. (1.2), p. 914.
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>.
%F a(n) = 2^(1+4*n-2*w(n)) with w(n) = A000120(n) = number of 1's in binary expansion of n.
%t a[n_] := 2^(4*n - 2*DigitCount[n, 2, 1] + 1); Array[a, 20, 0] (* _Amiram Eldar_, Aug 03 2023 *)
%o (PARI) a(n)=my(s=n); while(n>>=1, s+=n); 2<<(2*s) \\ _Charles R Greathouse IV_, Apr 07 2012
%Y Cf. A000120, A038534, A038535.
%Y Equals 2*A056982(n).
%K nonn,frac
%O 0,1
%A _Wouter Meeussen_, revised Jan 03 2001
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