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Question: Around Pascal's triangle

Question:Around Pascal's triangle

Markiyan Hirnyk 7809 Maple
combinatorics recurrence
September 13 2012
0

Let N(1, 1)=1 and N(1,k)=0 if k<>1. Let N(s+1,k) = N(s,k) + N(s,k-1) + N(s,k+1).
Acting in such a way, we obtain  the triangle
         1
       1,1,1
    1,2,3,2,1
  1,3,6,7,6,3,1
.................,
where only the nonzero terms are shown.
What is the explicit formula for N(s,k)? How to find it with Maple?
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