grandes-ecoles 2019 Q47

grandes-ecoles · France · centrale-maths2__psi Sequences and Series Evaluation of a Finite or Infinite Sum

For $j \in \mathbb{N}$, we denote by $Y_{n,j}$ the set of partitions whose first term $\alpha_1$ is less than or equal to $j$ and by $y_{n,j}$ the cardinality of $Y_{n,j}$; we set $y_{0,0} = 1$.
Calculate the $y_{n,j}$ for $1 \leqslant j \leqslant n \leqslant 5$ by presenting the results in the form of a table.

For $j \in \mathbb{N}$, we denote by $Y_{n,j}$ the set of partitions whose first term $\alpha_1$ is less than or equal to $j$ and by $y_{n,j}$ the cardinality of $Y_{n,j}$; we set $y_{0,0} = 1$.

Calculate the $y_{n,j}$ for $1 \leqslant j \leqslant n \leqslant 5$ by presenting the results in the form of a table.

Paper Questions

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