Eulerian(オイラー数) (math/fps/eulerian.hpp)

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Last update: 2024-04-27 01:27:28+09:00
Include: #include "math/fps/eulerian.hpp"

Code

/**
 * @brief Eulerian(オイラー数)
 */
template <template <typename> class FPS, typename Mint>
FPS<Mint> eulerian(int N) {
  vector<Mint> fact(N + 2), rfact(N + 2);
  fact[0] = rfact[N + 1] = 1;
  for (int i = 1; i <= N + 1; i++) fact[i] = fact[i - 1] * Mint(i);
  rfact[N + 1] /= fact[N + 1];
  for (int i = N; i >= 0; i--) rfact[i] = rfact[i + 1] * Mint(i + 1);
  FPS<Mint> A(N + 1), B(N + 1);
  for (int i = 0; i <= N; i++) {
    A[i] = fact[N + 1] * rfact[i] * rfact[N + 1 - i];
    if (i & 1) A[i] *= -1;
    B[i] = Mint(i + 1).pow(N);
  }
  return (A * B).pre(N + 1);
}

#line 1 "math/fps/eulerian.hpp"
/**
 * @brief Eulerian(オイラー数)
 */
template <template <typename> class FPS, typename Mint>
FPS<Mint> eulerian(int N) {
  vector<Mint> fact(N + 2), rfact(N + 2);
  fact[0] = rfact[N + 1] = 1;
  for (int i = 1; i <= N + 1; i++) fact[i] = fact[i - 1] * Mint(i);
  rfact[N + 1] /= fact[N + 1];
  for (int i = N; i >= 0; i--) rfact[i] = rfact[i + 1] * Mint(i + 1);
  FPS<Mint> A(N + 1), B(N + 1);
  for (int i = 0; i <= N; i++) {
    A[i] = fact[N + 1] * rfact[i] * rfact[N + 1 - i];
    if (i & 1) A[i] *= -1;
    B[i] = Mint(i + 1).pow(N);
  }
  return (A * B).pre(N + 1);
}