MathDB

f: \mathbb N \times \mathbb Z \rightarrow \mathbb Z

satisfy the given conditions

a)

f(0,0)\equal{}1 , f(0,1)\equal{}1 ,

b)

\forall k \notin \left\{0,1\right\}

f(0,k)\equal{}0 and

c)

\forall n \geq 1

and

k

, f(n,k)\equal{}f(n\minus{}1,k)\plus{}f(n\minus{}1,k\minus{}2n) find the sum \displaystyle\sum_{k\equal{}0}^{\binom{2009}{2}}f(2008,k)

Problem Statement