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 A178185 #24 Apr 14 2024 04:54:57
%S A178185 1,9,145,4641,297025,38019201,9732915457,4983252713985,
%T A178185 5102850779120641,10450638395639072769,42805814868537642061825,
%U A178185 350665235403060363770470401,5745299216843741000015387049985
%N A178185 Numerator of Sum_{k=1..n} 1/2^((k^2 + 3*k)/2).
%C A178185 Series of the kind m^((k^2 + 3*k)/2) from k=1 to n were studied by Bernoulli and Euler.
%H A178185 Vincenzo Librandi, <a href="/A178185/b178185.txt">Table of n, a(n) for n = 1..80</a>
%F A178185 a(n) = 2^(n+1)*a(n-1) + 1, a(1) = 1. - _Alexandre Herrera_, Mar 23 2024
%F A178185 a(n) ~ c * A036442(n+1) = c * 2^(n*(n+3)/2), where c = 2^(1/8) * EllipticTheta[2, 0, 1/Sqrt[2]] - 3 [in Mathematica] = 2^(1/8) * JacobiTheta2(0, 1/sqrt(2)) - 3 [in Maple] = 0.2832651213103077325876855404508588684521230759134794956... - _Vaclav Kotesovec_, Apr 10 2024
%t A178185 aa = {}; m = 1/2; sum = 0; Do[sum = sum + m^((n + 3) n/2); AppendTo[aa, Numerator[sum]], {n, 1, 20}]; aa
%t A178185 Numerator[Table[Sum[1/2^((k^2 + 3*k)/2), {k, 1, n}], {n, 1, 20}]] (* _Vaclav Kotesovec_, Apr 10 2024 *)
%o A178185 (PARI) a(n) = numerator(sum(k=1, n, (1/2)^((k^2+3*k)/2))); \\ _Michel Marcus_, Sep 09 2013
%Y A178185 Cf. A178184-A178193.
%Y A178185 Cf. A036442 (denominators).
%K A178185 nonn,frac
%O A178185 1,2
%A A178185 _Artur Jasinski_, May 21 2010