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 A056243 #24 Jul 29 2022 22:26:55
%S A056243 1,9,41,146,456,1312,3568,9312,23552,58112,140544,334336,784384,
%T A056243 1818624,4173824,9494528,21430272,48037888,107020288,237109248,
%U A056243 522715136,1147142144,2507145216,5458886656,11844714496,25618808832,55247372288
%N A056243 Third diagonal of triangle A056242.
%H A056243 F. K. Hwang and C. L. Mallows, <a href="http://dx.doi.org/10.1016/0097-3165(95)90097-7">Enumerating nested and consecutive partitions</a>, J. Combin. Theory Ser. A 70 (1995), no. 2, 323-333.
%F A056243 a(n) = Sum_{0<=j<=n-3} (-1)^(n-3-j)*binomial(n-3, j)*binomial(n+2j-1, 2j), for n>=3. - Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005
%F A056243 Conjecture: a(n) = 2^(-6+n)*(32-35*n+9*n^2). G.f.: x^3*(1+3*x-x^2)/(1-2*x)^3. - _Colin Barker_, Mar 20 2012
%p A056243 seq(add((-1)^(n-3-j)*binomial(n-3,j)*binomial(n+2*j-1,2*j),j=0..n-3),n=3..40); # Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005
%p A056243 T:=proc(n,k) local j: if k=1 then 1 elif k<=n then add((-1)^(k-1-j)*binomial(k-1,j)*binomial(n+2*j-1,2*j),j=0..k-1) else 0 fi end: seq(T(n,n-2),n=3..40); # Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005
%Y A056243 Cf. A056242.
%K A056243 nonn,easy
%O A056243 3,2
%A A056243 _Colin Mallows_, Aug 23 2000
%E A056243 More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005