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 A064984 #5 Mar 30 2012 18:37:42 %S A064984 1,0,1,1,0,2,0,2,0,1,3,0,10,0,2,0,23,0,20,0,2,45,0,196,0,70,0,4,0,132, %T A064984 0,154,0,28,0,1,315,0,1636,0,798,0,84,0,2,0,5067,0,7180,0,1806,0,120, %U A064984 0,2,14175,0,83754,0,50270,0,7392,0,330,0,4,0,146430,0,239327,0,74800,0 %N A064984 Triangle of coefficients T[n,m] of polynomials n, n^2, (n+2n^3)/3, n^2(2+n^2)/3, n(3+10n^2+2n^4)/15, etc. after multiplication by the denominators (A049606). %C A064984 These polynomials are P(1, n) = 2*Sum[k, {k,1,n-1}] + n, counting up to n and down again; P(2, m) = 2*Sum[P(1,n), {n,1,m-1}] + P(1,m), meaning up and down to n and this for n from 1 up to m and down again; etc. %e A064984 1+2+3+2+1 = 3^2, (1)+(1+2+1)+(1+2+3+2+1)+(1+2+1)+(1) = (n+2n^3)/3. %t A064984 CoefficientList[ #, n ]&/@(NestList[ ((2*Sum[ #, {n, k-1} ]+(#/. n->k)//Simplify)/.k->n)&, n, -1+16 ] Denominator[ 2^#/#!&/@Range[ 16 ] ]) %Y A064984 Row sums give A049606 again, final entry in each row seems to give A048896. %K A064984 nonn,tabl %O A064984 1,6 %A A064984 _Wouter Meeussen_, Oct 30 2001