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 A144250 #8 Nov 20 2022 10:52:48 %S A144250 1,1,1,1,3,2,1,6,10,6,1,10,30,42,23,1,15,70,168,207,106,1,21,140,504, %T A144250 1035,1166,567,1,28,252,1260,3795,6996,7371,3434 %N A144250 Eigentriangle, row sums = A125275, shifted. %C A144250 Row sums = A125273 shifted. A125273 = the eigensequence of triangle A085478. %C A144250 Right border = A125273: (1, 1, 2, 6, 23, 106, 567, 3434,...). Sum of n-th row terms = rightmost term in next row. %F A144250 Triangle read by rows, T(n,k) = A085478(n,k) * A125273(k). %F A144250 As infinite lower triangular matrices, A144250 = A085478 * (A125275 * 0^(n-k); where (A125275 * 0^(n-k)) = an infinite lower triangular matrix with A125275: (1, 1, 2, 6, 23, 106, 567, 3434,...) as the main diagonal and the rest zeros. %e A144250 First few rows of the triangle = %e A144250 1; %e A144250 1, 1; %e A144250 1, 3, 2; %e A144250 1, 6, 10, 6; %e A144250 1, 10, 30, 42, 23; %e A144250 1, 15, 70, 168, 207, 106; %e A144250 1, 21, 140, 504, 1035, 1166, 567; %e A144250 ... %e A144250 Row 4 = (1, 10, 30, 42, 23) = termwise products of (1, 10, 15, 7, 1) and (1, 1, 2, 6, 23) = (1*1, 10*1, 15*2, 7*6, 1*23); where (1, 10, 15, 7, 1) = row 4 of triangle A085478. Q %Y A144250 Cf. A125273, A085478. %K A144250 nonn,tabl,more %O A144250 0,5 %A A144250 _Gary W. Adamson_, Sep 16 2008 %E A144250 Corrected definition: Eigentriangle, row sums = A125273, shifted. - _Gary W. Adamson_, Nov 05 2008