cp's OEIS Frontend

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.

A185995 a(n) = 2^(binomial(2*n+2,3)/4).

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%I A185995 #20 Oct 18 2024 21:43:08
%S A185995 1,2,32,16384,1073741824,36028797018963968,
%T A185995 2475880078570760549798248448,
%U A185995 1393796574908163946345982392040522594123776,25711008708143844408671393477458601640355247900524685364822016
%N A185995 a(n) = 2^(binomial(2*n+2,3)/4).
%C A185995 Hankel transform of A185994.
%H A185995 G. C. Greubel, <a href="/A185995/b185995.txt">Table of n, a(n) for n = 0..20</a>
%F A185995 a(n) = Product_{k=0..n} (2^(2k+1))^(n-k).
%F A185995 a(n) = 2^A000330(n).
%F A185995 a(n) = 2^(1/6*n*(2*n^2+3*n+1)). - _Alexander R. Povolotsky_, Feb 13 2011
%t A185995 Table[2^(1/6*n*(2*n^2 + 3*n + 1)), {n, 0, 25}] (* _G. C. Greubel_, Feb 20 2017 *)
%t A185995 Table[2^(Binomial[2n+2,3]/4),{n,0,10}] (* _Harvey P. Dale_, Sep 13 2024 *)
%o A185995 (PARI) for(n=0,15, print1(2^(1/6*n*(2*n^2 + 3*n + 1)), ", ")) \\ _G. C. Greubel_, Feb 20 2017
%K A185995 nonn,easy
%O A185995 0,2
%A A185995 _Paul Barry_, Feb 08 2011