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 A186340 #8 Apr 18 2019 19:50:57
%S A186340 1,2,4,8,32,128,512,4096,32768,262144,4194304,67108864,1073741824,
%T A186340 34359738368,1099511627776,35184372088832,2251799813685248,
%U A186340 144115188075855872,9223372036854775808,1180591620717411303424,151115727451828646838272
%N A186340 a(n) = 2^A001840(n).
%C A186340 A factor in the Hankel transform A186339 of A186338.
%C A186340 a(n)*a(n-4) = 2*a(n-1)*a(n-3) = a(n-1)*a(n-3) + c(n)*a(n-2)^2, where c(3*n+2) = 2, c(3*n) = c(3*n+1) = 1 for all n in Z. - _Michael Somos_, Oct 19 2018
%F A186340 a(n)=2^floor((n+1)(n+2)/6).
%e A186340 G.f. = 1 + 2*x + 4*x^2 + 8*x^3 + 32*x^4 + 128*x^5 + 512*x^6 + ... - _Michael Somos_, Oct 19 2018
%t A186340 a[ n_] := 2^Quotient[ Binomial[n + 2, 2], 3]; (* _Michael Somos_, Oct 19 2018 *)
%o A186340 (PARI) {a(n) = 2^(binomial(n+2, 2)\3)}; /* _Michael Somos_, Oct 19 2018 */
%Y A186340 Cf. A058937.
%K A186340 nonn,easy
%O A186340 0,2
%A A186340 _Paul Barry_, Feb 18 2011