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 A117261 #18 Oct 17 2023 18:31:00
%S A117261 1,2,5,21,169,2705,86561,5539905,709107841,181531607297,
%T A117261 92944182936065,95174843326530561,194918079132734588929,
%U A117261 798384452127680876253185,6540365431829961738266091521,107157347235102093119751643480065,3511331954199825387348021853554769921
%N A117261 Row sums of triangle A117260.
%F A117261 a(n) = Sum_{k=0..n} 2^(n*(n-1)/2 - k*(k-1)/2).
%F A117261 G.f. A(x) satisfies: A(x) = 1/(1 - x) + x * A(2*x). - _Ilya Gutkovskiy_, Jun 06 2020
%F A117261 a(n) = a(n-1) * 2^(n-1) + 1 for n > 0 and a(0) = 1. - _Werner Schulte_, Oct 17 2023
%t A117261 Table[Sum[2^((n(n-1))/2-(k(k-1))/2),{k,0,n}],{n,0,20}] (* _Harvey P. Dale_, Jul 05 2023 *)
%o A117261 (PARI) a(n)=sum(k=0,n,2^((n-k)*(n+k-1)/2))
%Y A117261 Cf. A073587, A117260, A117263.
%K A117261 nonn
%O A117261 0,2
%A A117261 _Paul D. Hanna_, Mar 14 2006