在组合数学中,施罗德数用来描述从(0,0)到(n,n)的格路中,只能使用(1,0)、(0,1)、(1,1)三种移动方式,始终位于对角线下方且不越过对角线的路径数

DECLARE @n INT =10
DECLARE @i INT
DECLARE @rst INT 
DECLARE @old INT=1

CREATE TABLE #rst
(
	i INT ,
	rst int
)

INSERT INTO #rst values(1,1)
 
SET @i=2
WHILE @i<=@n 
BEGIN 
	SET @rst=0
	SELECT @rst=@rst+a.rst*b.rst FROM #rst a 
	INNER JOIN (
		SELECT *,ROW_NUMBER() OVER(ORDER BY i desc) j  FROM #rst
	) b ON a.i = b.j

	SET @rst=@rst+@old
 
	INSERT INTO #rst values(@i,@rst)
	SET @i=@i+1
	SET @old=@rst 
END 

SELECT *   FROM #rst

DROP TABLE #rst