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 A114202 #12 Jan 29 2019 07:22:35
%S A114202 1,1,1,1,2,1,1,3,3,1,1,4,8,4,1,1,5,16,16,5,1,1,6,27,42,27,6,1,1,7,41,
%T A114202 87,87,41,7,1,1,8,58,156,216,156,58,8,1,1,9,78,254,456,456,254,78,9,1,
%U A114202 1,10,101,386,860,1122,860,386,101,10,1
%N A114202 A Pascal-Jacobsthal triangle.
%C A114202 Row sums are A114203. T(2n,n) is A114204. Inverse has row sums 0^n.
%H A114202 Paul Barry, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Barry/barry91.html">On Integer-Sequence-Based Constructions of Generalized Pascal Triangles</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.
%F A114202 As a number triangle, with J(n) = A001045(n):
%F A114202 T(n, k) = Sum_{i=0..n-k} C(n-k, i)*C(k, i)*J(i);
%F A114202 T(n, k) = Sum_{i=0..n} C(n-k, n-i)*C(k, i-k)*J(i-k);
%F A114202 T(n, k) = Sum_{i=0..n} C(k, i)*C(n-k, n-i)*J(k-i) if k <= n, and 0 otherwise.
%F A114202 As a square array, with J(n) = A001045(n):
%F A114202 T(n, k) = Sum_{i=0..n} C(n, i)C(k, i)*J(i);
%F A114202 T(n, k) = Sum_{i=0..n+k} C(n, n+k-i)*C(k, i-k)*J(i-k);
%F A114202 Column k has g.f. (Sum_{i=0..k} C(k, i)*J(i+1)*(x/(1 - x))^i)*x^k/(1 - x).
%e A114202 Triangle begins
%e A114202 1;
%e A114202 1, 1;
%e A114202 1, 2, 1;
%e A114202 1, 3, 3, 1;
%e A114202 1, 4, 8, 4, 1;
%e A114202 1, 5, 16, 16, 5, 1;
%e A114202 1, 6, 27, 42, 27, 6, 1;
%e A114202 1, 7, 41, 87, 87, 41, 7, 1;
%e A114202 ...
%K A114202 easy,nonn,tabl
%O A114202 0,5
%A A114202 _Paul Barry_, Nov 16 2005