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.

A230049 Triangle such that the g.f. of column k equals 1/(1-x)^(k^3) for k>=0, as read by rows.

This page as a plain text file.
%I A230049 #8 Apr 26 2016 12:42:52
%S A230049 1,0,1,0,1,1,0,1,8,1,0,1,36,27,1,0,1,120,378,64,1,0,1,330,3654,2080,
%T A230049 125,1,0,1,792,27405,45760,7875,216,1,0,1,1716,169911,766480,333375,
%U A230049 23436,343,1,0,1,3432,906192,10424128,10668000,1703016,58996,512,1,0,1,6435,4272048,119877472,275234400,93240126,6784540,131328,729,1
%N A230049 Triangle such that the g.f. of column k equals 1/(1-x)^(k^3) for k>=0, as read by rows.
%F A230049 T(n, k) = binomial(k^3+n-k-1, n-k) for n>=k>=0.
%e A230049 Triangle begins:
%e A230049 1;
%e A230049 0, 1;
%e A230049 0, 1, 1;
%e A230049 0, 1, 8, 1;
%e A230049 0, 1, 36, 27, 1;
%e A230049 0, 1, 120, 378, 64, 1;
%e A230049 0, 1, 330, 3654, 2080, 125, 1;
%e A230049 0, 1, 792, 27405, 45760, 7875, 216, 1;
%e A230049 0, 1, 1716, 169911, 766480, 333375, 23436, 343, 1;
%e A230049 0, 1, 3432, 906192, 10424128, 10668000, 1703016, 58996, 512, 1;
%e A230049 0, 1, 6435, 4272048, 119877472, 275234400, 93240126, 6784540, 131328, 729, 1; ...
%o A230049 (PARI) {T(n, k) = polcoeff(1/(1-x+x*O(x^n))^(k^3), n-k)}
%o A230049 for(n=0,12,for(k=0,n,print1(T(n,k),", "));print(""))
%o A230049 (PARI) {T(n, k) = binomial(k^3+n-k-1, n-k)}
%o A230049 for(n=0,12,for(k=0,n,print1(T(n,k),", "));print(""))
%Y A230049 Cf. A230050 (row sums), A229711.
%K A230049 nonn,tabl
%O A230049 0,9
%A A230049 _Paul D. Hanna_, Oct 06 2013