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 A125100 #13 Nov 14 2019 09:42:17 %S A125100 1,2,1,3,4,2,4,9,9,3,5,16,24,16,5,6,25,50,50,30,8,7,36,90,120,105,54, %T A125100 13,8,49,147,245,280,210,98,21,9,64,224,448,630,616,420,176,34,10,81, %U A125100 324,756,1260,1512,1344,828,315,55,11,100,450,1200,2310,3276,3570,2880,1620 %N A125100 Triangle read by rows: T(n,k) = Fibonacci(k+1)*binomial(n,k) + (k+1)*binomial(n,k+1) (0 <= k <= n). %C A125100 Binomial transform of the bidiagonal matrix with the Fibonacci numbers (1, 1, 2, 3, 5, 8, ...) in the main diagonal and (1, 2, 3, ...) in the subdiagonal. %C A125100 Sum of terms in row n = n*2^(n-1) + Fibonacci(2n+1) (A081663). %e A125100 First few rows of the triangle: %e A125100 1; %e A125100 2, 1; %e A125100 3, 4, 2; %e A125100 4, 9, 9, 3; %e A125100 5, 16, 24, 16, 5; %e A125100 6, 25, 50, 50, 30, 8; %e A125100 7, 36, 90, 120, 105, 54, 13; %e A125100 8, 49, 147, 245, 280, 210, 98, 21; %e A125100 ... %p A125100 with(combinat): T:=(n,k)->binomial(n,k)*fibonacci(k+1)+(k+1)*binomial(n,k+1): for n from 0 to 11 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form %Y A125100 Cf. A081663, A081659. %Y A125100 Cf. A000045. %K A125100 nonn,tabl %O A125100 0,2 %A A125100 _Gary W. Adamson_, Nov 20 2006 %E A125100 Edited by _N. J. A. Sloane_, Nov 29 2006