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.

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

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%I A057280 #3 Mar 31 2012 13:20:04
%S A057280 2,17,5,225,120,15,4080,3050,700,50,94440,89225,28625,3775,175,
%T A057280 2666880,3006000,1208975,223175,19225,625,89016480,115299900,54824650,
%U A057280 12689800,1537100,93500,2250,3430929600,4973077800,2695596850,737744125
%N A057280 Coefficient triangle of polynomials (rising powers) related to Fibonacci convolutions. Companion triangle to A057995.
%C A057280 The row polynomials are q(k,x) := sum(a(k,m)*x^m,m=0..k), k=0,1,2,...
%C A057280 The k-th convolution of F0(n) := A000045(n+1), n >= 0, (Fibonacci numbers 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 p(k,n) := sum(b(k,m)*n^m,m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A057995(k,m).
%e A057280 k=2: F2(n)=((16+5*n)*(n+1)*F0(n+1)+(17+5*n)*(n+2)*F0(n))/50, cf. A001628.
%Y A057280 Cf. A000045, A037027, A057995.
%K A057280 nonn,tabl
%O A057280 0,1
%A A057280 _Wolfdieter Lang_, Sep 13 2000