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 A063422 #5 Mar 31 2012 13:20:06
%S A063422 1,1,1,1,1,4,-6,4,-1,3,-2,-2,3,-1,2,2,-8,7,-2,1,6,-14,11,-3,10,-20,15,
%T A063422 -4,6,2,-37,65,-56,28,-8,1,3,16,-61,78,-42,0,12,-6,1,1,22,-57,35,42,
%U A063422 -84,60,-21,3,20,-25,-64,196,-224,136,-44,6,10,35,-219,420
%N A063422 Coefficient array for certain numerator polynomials N5(n,x), n >= 0 (rising powers of x) used for quintinomials (also called pentanomials).
%C A063422 The g.f. of column k of array A035343(n,k) (quintinomial coefficients) is (x^(ceiling(k/4)))*N5(k,x)/(1-x)^(k+1).
%C A063422 The sequence of degrees for the polynomials N5(n,x) is [0, 0, 0, 0, 0, 3, 4, 4, 4, 3, 7, 8, 8, 7, 7,...] for n >= 0.
%C A063422 Row sums N5(n,1)=1 for all n.
%F A063422 a(n, m) = [x^m]N5(n, x), n, m >= 0, with N5(n, x)= sum(((1-x)^(j-1))*(x^(b(c(n), j)))*N5(n-j, x), j=1..4), N5(n, x)= 1 for n=0..3 and b(c(n), j) := 1 if 1<= j <= c(n) else 0, with c(n) := 3 if mod(n, 4)=0 else c(n) := mod(n, 4)-1; (hence b(0, j)=0, j=1..4).
%e A063422 {1}; {1}; {1}; {1}; {1}; {4,-6,4,-1}; {3,-2,-2,3,-1}; {2,2,-8,7,-2}; {1,6,-14,11,-3}; ...
%e A063422 c=2: b(2,1)= 1 = b(2,2), b(2,3)= 0 =b(2,4).
%e A063422 N5(6,x)=3-2*x-2*x^2+3*x^3-x^4.
%K A063422 sign,easy,tabf
%O A063422 0,6
%A A063422 _Wolfdieter Lang_, Jul 27 2001