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%I #20 Jan 24 2016 02:50:45
%S 1,1,4,56,1712,92800,7918592,984237056,168662855680,38238313152512,
%T 11106033743298560,4026844843819663360,1784377436257886142464,
%U 949324216111786046259200,597340801661667138076672000,438858704839955952346364641280
%N Chocolate-2 numbers.
%C Given a 2-by-n chocolate bar, a(n) is the number of ways to break it into 2n unit pieces where each break occurs along a gridline. Order matters, and the pieces are distinguishable.
%C For n>1, a(n) is divisible by 2^n.
%H Caleb Ji, Tanya Khovanova, Robin Park, Angela Song, <a href="http://arxiv.org/abs/1509.06093">Chocolate Numbers</a>, arXiv:1509.06093 [math.CO], 2015.
%H Caleb Ji, Tanya Khovanova, Robin Park, Angela Song, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Khovanova/khova9.html">Chocolate Numbers</a>, Journal of Integer Sequences, Vol. 19 (2016), #16.1.7.
%F a(n) = A(n,2) with A(m,n)=1 for max(m,n)<2 and A(m,n) = Sum_{i=1..m-1} C(m*n-2,i*n-1) *A(i,n) *A(m-i,n) + Sum_{i=1..n-1} C(m*n-2,i*m-1) *A(m,i) *A(m,n-i) else.
%e For n = 2, there are two ways for the first break: breaking it horizontally or vertically. After that we need two more breaks that can be done in any order. Thus a(2) = 4.
%Y Cf. A257281, A261746, A261964.
%K nonn
%O 0,3
%A _Caleb Ji_, _Tanya Khovanova_, _Robin Park_, _Angela Song_, Aug 30 2015
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