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 A351145 #13 Feb 03 2022 04:56:12
%S A351145 1,4,6,15,27,29,56,112,128,131,210,450,540,570,572,792,1782,2222,2420,
%T A351145 2444,2448,3003,7007,9009,10101,10283,10339,10341,11440,27456,36192,
%U A351145 41652,42772,43252,43284,43288,43758,107406,144534,170238,176358,179622,179928,180000,180003
%N A351145 Triangle T(n,m) read by rows: Sum_{k=1..m} binomial(2*n, n+k)*d(k), m<=n, with d(k)=A000005(k).
%C A351145 Exercise 52 in chapter 5.2.2 of Knuth's TAOCP 3 asks: "What is the asymptotic behavior of the sum S_n = Sum_{t>=1} binomial(2n,n+t)*d(t)?" and mentions "This question arises in connection with the analysis of a tree traversal algorithm, exercise 2.3.1-11."
%D A351145 D. E. Knuth, The Art of Computer Programming Second Edition. Vol. 3, Sorting and Searching. Chapter 5.2.2 Sorting by Exchanging, pages 138, 637 (answer to exercise 52). Addison-Wesley, Reading, MA, 1998.
%e A351145 The triangle begins:
%e A351145 1;
%e A351145 4, 6;
%e A351145 15, 27, 29;
%e A351145 56, 112, 128, 131;
%e A351145 210, 450, 540, 570, 572;
%e A351145 792, 1782, 2222, 2420, 2444, 2448;
%e A351145 3003, 7007, 9009, 10101, 10283, 10339, 10341;
%e A351145 11440, 27456, 36192, 41652, 42772, 43252, 43284, 43288;
%t A351145 T[n_, m_] := Sum[Binomial[2*n, n + k] * DivisorSigma[0, k], {k, 1, m}]; Table[T[n, m], {n, 1, 9}, {m, 1, n}] // Flatten (* _Amiram Eldar_, Feb 02 2022 *)
%o A351145 (PARI) for(n=1,10,for(m=1,n,my(s=sum(t=1,m,binomial(2*n,n+t)*numdiv(t)));print1(s,", ")))
%Y A351145 Cf. A000005, A001791 (first column), A351146 (diagonal).
%K A351145 nonn,tabl
%O A351145 1,2
%A A351145 _Hugo Pfoertner_, Feb 02 2022