%I #25 Mar 23 2022 16:18:59

%S 1,1,1,25,16,841,16641,4225,13608721,264517696,12925188721,

%T 5677664356225,49020596163841,158432514799144041,62586636021357187216,

%U 1870098771536627436025,41998153797159031581158401,15402543997324146892198790401

%N Denominator of x-coordinate of (2n)*P where P = (0,0) is the generator for rational points on the curve y^2 + y = x^3 - x.

%H Seiichi Manyama, <a href="/A028937/b028937.txt">Table of n, a(n) for n = 1..106</a>

%H LMFDB, <a href="https://www.lmfdb.org/EllipticCurve/Q/37/a/1">Elliptic Curve 37.a1 (Cremona label 37a1)</a>

%H B. Mazur, <a href="https://doi.org/10.1090/S0273-0979-1986-15430-3">Arithmetic on curves</a>, Bull. Amer. Math. Soc. 14 (1986), 207-259; see p. 225.

%F P=(0, 0), 2P=(1, 0); if kP=(a, b) then (k+1)P = (a' = (b^2 - a^3)/a^2, b' = -1 - b*a'/a).

%F a(n) = A028941(2n). - _Seiichi Manyama_, Nov 19 2016

%F a(n) = a(-n) = b(n)*b(n+3) - b(n+1)*b(n+2) for all n in Z where b(n) = A006720(n). - _Michael Somos_, Mar 23 2022

%e a(4) = 25 where 8P = (21/25, -69/125).

%o (PARI) a(n)=denominator(ellmul(E,[0,0],2*n)[1]) \\ _Charles R Greathouse IV_, Mar 23 2022

%Y Cf. A006720, A051138, A028936 (numerator), A028938, A028939, A028941.

%K nonn,frac

%O 1,4

%A _N. J. A. Sloane_