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 A193451 #16 Jun 04 2014 17:03:56 %S A193451 0,0,1,0,3,3,0,5,8,2,0,7,17,14,6,0,9,30,39,24,3,0,11,47,83,75,33,9,0, %T A193451 13,68,152,184,126,48,4,0,15,93,252,384,354,198,60,12,0,17,122,389, %U A193451 716,830,620,290,80,5,0,19,155,569,1229,1718,1610,1010,410,95,15 %N A193451 Triangle of a binomial convolution sum related to Jacobsthal numbers. %C A193451 Row sum is A193449(n) = n*A001045(n+1). %F A193451 T(n,k)= sum( (-1)^(j+k)*(j+k)*C(n-k+j,j), j=0..k). %e A193451 Triangle starts: %e A193451 0; %e A193451 0, 1; %e A193451 0, 3, 3; %e A193451 0, 5, 8, 2; %e A193451 0, 7, 17, 14, 6; %e A193451 0, 9, 30, 39, 24, 3; %e A193451 ... %o A193451 (PARI) T(n,k)= sum(j=0, k, (-1)^(j+k)*(j+k)*binomial(n-k+j,j)); \\ _Michel Marcus_, Jun 04 2014 %Y A193451 Cf. A193449, A193450, A001045. %K A193451 nonn,easy,tabl %O A193451 0,5 %A A193451 _Olivier Gérard_, Jul 26 2011