This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A222207 #16 Feb 25 2017 16:44:55
%S A222207 2,12,788,7636,874202,10018884,1445893544,2954512034024,
%T A222207 38700329118256,93229749133527532,17540746936557672236,
%U A222207 243284404062970619608,47694250379410432495952,136236017676683906365850456,404504597532158799519693872144,5856120097210409121404621878992,18102352585707069737371994385420772,3894254646848417473467131712404310728
%N A222207 Morley quotients: (2^(2*p-2) - (-1)^((p-1)/2)*binomial(p-1,(p-1)/2)) / p^3, where p = prime(n) and n >= 3.
%C A222207 Morley (1894/95) proved 2^(2*p-2) == (-1)^((p-1)/2)*binomial(p-1,(p-1)/2) mod p^3 for all primes p > 3.
%C A222207 Morley quotients are even, since 2^(2*p-2) and binomial(p-1,(p-1)/2) are even and p^3 is odd.
%H A222207 Vincenzo Librandi, <a href="/A222207/b222207.txt">Table of n, a(n) for n = 3..200</a>
%H A222207 C. Aebi, G. Cairns, <a href="http://arxiv.org/abs/1302.3678">Morley’s other miracle</a>, Math. Mag., 85 (2012), 205-211.
%H A222207 F. Morley, <a href="http://www.jstor.org/stable/1967516">Note on the Congruence 2^4n == (-1)^n*(2n)!/(n!)^2 where 2n+1 is a prime</a>, Annals of Mathematics, Vol. 9 (1894 - 1895), pp. 168-170.
%e A222207 prime(3) = 5, so a(3) = (2^(2*5-2) - (-1)^((5-1)/2)*binomial(5-1,(5-1)/2))/5^3 = (2^8 - binomial(4,2))/5^3 = (256-6)/125 = 2.
%t A222207 m[p_] := (2^(2*p-2) - (-1)^((p-1)/2)*Binomial[p-1, (p-1)/2])/p^3; Table[ m[ Prime[n]], {n, 3, 20}]
%Y A222207 Cf. A007619, A007663, A034602, A197630, A197633.
%K A222207 nonn
%O A222207 3,1
%A A222207 _Jonathan Sondow_, Feb 22 2013