cp's OEIS Frontend

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.

A057995 Coefficient triangle of polynomials (rising powers) related to Fibonacci convolutions. Companion triangle to A057280.

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%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