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 A144025 #12 Apr 29 2025 16:07:20 %S A144025 1,1,1,2,1,2,4,2,2,5,9,4,4,5,13,21,9,8,10,13,35,51,21,18,20,26,35,96, %T A144025 127,51,42,45,52,70,96,267,323,127,102,105,117,140,192,267,750,835, %U A144025 323,254,255,273,315,384,534,750,2123,2188,835,646,635,663,735,864,1068,1500,2123,6046 %N A144025 Eigentriangle by rows, A001006(n-k)*A005773(k); 0<=k<=n. %C A144025 Left border = Motzkin numbers, A001006. %C A144025 Right border = A005773. %C A144025 Row sums = A005773 shifted: (1, 2, 5, 13, 35, 96, 267,...). %C A144025 Sum of n-th row terms = rightmost term of next row. %F A144025 Eigentriangle by rows: T(n,k) = A001006(n-k)*A005773(k); 0<=k<=n. %e A144025 First few rows of the triangle = %e A144025 1; %e A144025 1, 1; %e A144025 2, 1, 2; %e A144025 4, 2, 2, 5; %e A144025 9, 4, 4, 5, 13; %e A144025 21, 9, 8, 10, 13, 35; %e A144025 51, 21, 18, 20, 26, 35, 96; %e A144025 127, 51, 42, 45, 52, 70, 96, 267; %e A144025 323, 127, 102, 105, 117, 140, 192, 267, 750; %e A144025 835, 323, 254, 255, 273, 315, 384, 534, 750, 2123; %e A144025 ... %e A144025 Row 3 = (4, 2, 2, 5) = termwise product of (4, 2, 1, 1) and the first 4 terms of A005773: (1, 1, 2, 5) = (4*1, 2*1, 1*2, 1*5). (4, 2, 1, 1) = the first 4 terms of A001066, reversed. %Y A144025 Cf. A001066, A005773. %K A144025 nonn,tabl %O A144025 0,4 %A A144025 _Gary W. Adamson_, Sep 07 2008 %E A144025 a(53) corrected by _Georg Fischer_, Apr 29 2025