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 A096646 #9 Apr 16 2014 00:46:06 %S A096646 1,1,1,1,1,3,4,3,1,1,5,11,14,11,5,1,1,7,22,41,50,41,22,7,1,1,9,37,92, %T A096646 154,182,154,92,37,9,1,1,11,56,175,375,582,672,582,375,175,56,11,1 %N A096646 Triangle (read by rows) where the number of row entries increases by steps of 2 and the entries are stacked in a rectangular fashion. The end entries = 1. Rest of entries in the n-th row are the sum of the entries directly above and to the left and right in all previous rows (total of 3*(n-1) entries). %C A096646 The row sums are 1,3, then 2^(2*(n-2)) * 3. (I.e., A002001 a(n) = 3*4^(n-1), n>0; a(0)=1.) The n-th row is the (2n-1)st row of A072405 (Triangle of C(n,k)-C(n-2,k-1)). %F A096646 G.f.: 1/[(1-z(1+w+w^2))(1-wz)]. Partial sums of trinomial array A027907. - _Ralf Stephan_, Jan 09 2005 %e A096646 ......................1.................... %e A096646 ..................1...1...1................ %e A096646 ..............1...3...4...3...1............ %e A096646 ..........1...5..11..14..11...5...1........ %e A096646 ......1...7..22..41..50..41..22...7..1..... %e A096646 ...1..9..37..92.154.182.154..92..37..9..1.. %e A096646 1.11.56.175.375.582.672.582.375.175.56.11.1 %Y A096646 Cf. A002001, A072405. %K A096646 nonn,tabf %O A096646 1,6 %A A096646 _Gerald McGarvey_, Aug 14 2004