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Fancy polynomial

Author: anonymous
Problem has been solved: 17 times

Русский язык | English Language



Let $n = 228667228667$. Polynomial of $n$ variables $f(x_1, x_2, \ldots, x_n)$ with complex coefficients is such that \[f(a_1, a_2, \ldots, a_n) = \prod_{i = 1}^{n} (a_i - i + 1)^2\] for all integers $i \leq a_i \leq i + 1$. Moreover, the power of $x_i$ in each monomial doesn't exceed 1 for all $1 \leq i \leq n$. Let the coefficient of monomial $x_1 x_2 \ldots x_n$ in $f$ be equal to $c$. Find $c \pmod{10^9 + 7}$. It is guaranteed that $c \in \mathbb{Z}$.





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