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 A377809 #20 Nov 09 2024 17:28:12
%S A377809 2,5,5,9,9,9,14,14,14,14,20,20,20,20,20,27,27,27,27,27,27,35,35,35,35,
%T A377809 35,35,35,44,44,44,44,44,44,44,44,54,54,54,54,54,54,54,54,54,65,65,65,
%U A377809 65,65,65,65,65,65,65,77,77,77,77,77,77,77,77,77,77,77,90
%N A377809 k*(k+3)/2 appears k times.
%F A377809 a(n) = A002024(n)*(A002024(n)+3)/2.
%F A377809 First difference of A119713.
%F A377809 T(n,k) = A000096(n) for 1 <= k <= n. - _Alois P. Heinz_, Nov 09 2024
%F A377809 G.f.: x*y*(2 - x*y)/((1 - x)*(1 - x*y)^3). - _Stefano Spezia_, Nov 09 2024
%e A377809 As triangle:
%e A377809 2;
%e A377809 5, 5;
%e A377809 9, 9, 9;
%e A377809 14, 14, 14, 14;
%e A377809 20, 20, 20, 20, 20;
%e A377809 ...
%t A377809 s={};Do[AppendTo[s,Table[k(k+3)/2,k]],{k,12}];Flatten[s] (* _James C. McMahon_, Nov 09 2024 *)
%o A377809 (Python)
%o A377809 from math import isqrt
%o A377809 def A377809(n): return (r:=(m:=isqrt(k:=n<<1))+(k>m*(m+1)))*(r+3)>>1
%Y A377809 Cf. A000096, A002024, A119713.
%K A377809 nonn,easy,tabl
%O A377809 1,1
%A A377809 _Chai Wah Wu_, Nov 08 2024