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