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 A057995 #3 Mar 31 2012 13:20:04 %S A057995 1,16,5,300,160,20,6840,4850,1075,75,186120,159650,48175,6100,275, %T A057995 5916240,5846700,2168650,379700,31550,1000,215717040,238437900, %U A057995 103057800,22426825,2605175,153875,3625,8888140800,10772348400 %N A057995 Coefficient triangle of polynomials (rising powers) related to Fibonacci convolutions. Companion triangle to A057280. %C A057995 The row polynomials are p(k,x) := sum(a(k,m)*x^m,m=0..k), k=0,1,2,... %C A057995 The k-th convolution of F0(n) := A000045(n+1) n >= 0, (Fibonacci starting with F0(0)=1) with itself is Fk(n) := A037027(n+k,k) = (p(k-1,n)*(n+1)*F0(n+1) + q(k-1,n)*(n+2)*F0(n))/(k!*5^k)), k=1,2,..., where the companion polynomials q(k,n) := sum(b(k,m)*n^m,m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A057280). %e A057995 k=2: F2(n)=((16+5*n)*(n+1)*F0(n+1)+(17+5*n)*(n+2)*F0(n))/50, cf. A001628. %Y A057995 Cf. A000045, A037027, A057280. %K A057995 nonn,tabl %O A057995 0,2 %A A057995 _Wolfdieter Lang_, Sep 13 2000