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 A076744 #10 Apr 15 2025 08:28:29
%S A076744 4,72,4176,731808,381879360,592267282560,2733202405059840,
%T A076744 37590062966534453760,1542797317119230338360320,
%U A076744 189160927199005707074274969600,69339320764681731806436884240486400,76034016779649931607383549266935620608000
%N A076744 Related to the expected length of the shortest nonintersecting path through n points on a Sierpiński Gasket from corner to corner.
%C A076744 Original name: This sequence with the appropriate denominator (product of (2*3^k-3) k=0..n) produces the expected length of shortest nonintersecting path through n points on a Sierpiński Gasket from corner to corner.
%C A076744 Does b(n) / n^(1-log(2)/log(3)) -> constant?
%F A076744 a(n) = b(n) * c(n) where b(n) = Sum_{k=0..n} (-1)^k * binomial(n, k) / (2*3^k-3) and c(n) = Product_{k=0..n} (2*3^k-3).
%p A076744 b:=n->sum(binomial(n,k)*(-1)^k/(2*3^k-3),k=0..n);
%p A076744 c:=n->product(2*3^k-3,k=0..n);
%p A076744 a:=n->b(n)*c(n);
%p A076744 seq(a(n),n=1..12);
%K A076744 nonn
%O A076744 1,1
%A A076744 _Nathan B. Shank_, Nov 11 2002
%E A076744 Revised by _Sean A. Irvine_, Apr 14 2025