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 A122441 #12 Aug 22 2025 14:55:02
%S A122441 1,-1,1,-5,25,-141,849,-5349,34825,-232445,1582081,-10938709,76616249,
%T A122441 -542472685,3876400305,-27919883205,202480492905,-1477306676445,
%U A122441 10836099051105,-79861379898165,591082795606425,-4391625157145805,32742445489969425,-244889639907014565
%N A122441 Expansion of 2*(sqrt(1+8x)-3)/(sqrt(1+8x)-5).
%H A122441 Robert Israel, <a href="/A122441/b122441.txt">Table of n, a(n) for n = 0..1108</a>
%F A122441 a(n) = -hypergeometric([1-n, n], [-n], -2) if n>0. - _Peter Luschny_, Nov 30 2014
%F A122441 (4 + 8*n)*a(n) + (-10 - 23*n)*a(n + 1) + (-3*n - 6)*a(n + 2) = 0. - _Robert Israel_, Aug 22 2025
%p A122441 f:= gfun:-rectoproc({(4 + 8*n)*a(n) + (-10 - 23*n)*a(n + 1) + (-3*n - 6)*a(n + 2), a(0) = 1, a(1) = -1, a(2) = 1},a(n),remember):
%p A122441 map(f, [$0..40]); # _Robert Israel_, Aug 22 2025
%o A122441 (Sage)
%o A122441 def a(n):
%o A122441 if n==0: return 1
%o A122441 return -hypergeometric([1-n, n], [-n], -2).simplify()
%o A122441 [a(n) for n in range(21)] # _Peter Luschny_, Nov 30 2014
%Y A122441 Row sums of A122440.
%Y A122441 Cf. A064311.
%K A122441 easy,sign,changed
%O A122441 0,4
%A A122441 _Paul Barry_, Sep 05 2006