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 A127774 #19 Jun 10 2025 10:55:36 %S A127774 1,0,4,0,0,10,0,0,0,20,0,0,0,0,35,0,0,0,0,0,56,0,0,0,0,0,0,84,0,0,0,0, %T A127774 0,0,0,120,0,0,0,0,0,0,0,0,165,0,0,0,0,0,0,0,0,0,220,0,0,0,0,0,0,0,0, %U A127774 0,0,286,0,0,0,0,0,0,0,0,0,0,0,364 %N A127774 Triangle read by rows: row n consists of n-1 zeros followed by A000292(n). %C A127774 Essentially triangle T(n,k), read by rows, given by (0,0,0,0,0,0,0,...) DELTA (4,-3/2,5/6,-1/3,3/5,-1/10,1/2,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938. - _Philippe Deléham_, Nov 14 2011 %F A127774 G.f.: 1/((x*y-1)^4). - _R. J. Mathar_, Aug 12 2015 %e A127774 First few rows of the triangle are: %e A127774 1; %e A127774 0, 4; %e A127774 0, 0, 10; %e A127774 0, 0, 0, 20; %e A127774 0, 0, 0, 0, 35; %e A127774 ... %o A127774 (Python) %o A127774 from math import isqrt %o A127774 from sympy.ntheory.primetest import is_square %o A127774 def A127774(n): return (a:=(m:=isqrt(k:=n<<1))+(k>m*(m+1)))*(a+1)*(a+2)//6 if is_square((n<<3)+1) else 0 # _Chai Wah Wu_, Jun 09 2025 %Y A127774 Cf. A000292, A127648, A127773. %K A127774 nonn,tabl,easy %O A127774 1,3 %A A127774 _Gary W. Adamson_, Jan 28 2007 %E A127774 More terms from _Michel Marcus_, Jun 10 2025