を満たす$d$次多項式の列$f_n(i),\ldots,f_1(i),f_0(i)$を返すライブラリ。他のライブラリとの関係上、列が降順($(f_n,\ldots,f_1,f_0)$の順番)になっているのに注意。
Constant Function
a_{k+1} = a_{k}
Identity Function (a_i = i + 1)
(k + 1)a_{k+1} = (k + 2)a_{k}
Factorial
a_{k+1} = (k + 1)a_{k}
Inversion of Factorial
(k + 1)a_{k+1} = a_{k}
Binomial (a_i = binom(i + 3, 3))
(k + 1)a_{k+1} = (k + 4)a_{k}
Montmort Number
a_{k+2} = (k + 1)a_{k+1} + (k + 1)a_{k}
Catalan Number
(k + 2)a_{k+1} = (4k + 2)a_{k}
Motzkin Number
(k + 4)a_{k+2} = (2k + 5)a_{k+1} + (3k + 3)a_{k}
Schroder number
(k + 3)a_{k+2} = (6k + 9)a_{k+1} + (998244352k + 0)a_{k}