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%I #10 Sep 08 2022 08:46:24
%S 2,98,4802,235298,11529602,564950498,27682574402,1356446145698,
%T 66465861139202,3256827195820898,159584532595224002,
%U 7819642097165976098,383162462761132828802,18774960675295508611298,919973073089479921953602,45078680581384516175726498,2208855348487841292610598402
%N a(n) = 2*49^n.
%C x = A324265(n) and y = a(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 7^(6*n+1) = 4*y^3 (see Theorem 2.1 in Chakraborty, Hoque and Sharma).
%H K. Chakraborty, A. Hoque, R. Sharma, <a href="https://arxiv.org/abs/1812.11874">Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations</a>, arXiv:1812.11874 [math.NT], 2018.
%F O.g.f.: 2/(1 - 49*x).
%F E.g.f.: 2*exp(49*x).
%F a(n) = 49*a(n-1) for n > 0.
%F a(n) = (49/2)*(A109808(n))^2.
%e For A324265(0) = 5 and a(0) = 2, 5^2 + 7 = 32 = 4*2^3.
%p a:=n->2*49^n: seq(a(n), n=0..20);
%t 2*49^Range[0,20]
%o (GAP) List([0..20], n->2*49^n);
%o (Magma) [2*49^n: n in [0..20]];
%o (PARI) a(n) = 2*49^n;
%Y Cf. A324265 (5*343^n), A000290 (n^2), A000578 (n^3), A109808 (2*7^(n-1)).
%K nonn,easy
%O 0,1
%A _Stefano Spezia_, Feb 20 2019
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