일반항을 사용하는 경우

파스칼 삼각형의 공식은

nCr = n! / ( r! * (n-r)! ) 이고

 

n! 은 exp(sum(ln(n)) 으로 구할 수 있으므로

 

with base_line as

(

    select

        level-1 l

    from    dual

    connect by  level <= 10

)

, base_fct as

(

    select

        a.l+1 l

        ,round(exp(sum(ln(a.l+1)) over (order by a.l))) fct

    from    base_line a

    union all

    select

        0

        ,1

    from    dual

)

, base_frame as

(

    select

        b.l n

        ,a.l k

    from    base_line a

            , base_line b

    where   a.l <= b.l

)

select

    a.n

    , a.k

    , b.fct / ( c.fct * d.fct ) n_c_k

from    base_frame a

        , base_fct b

        , base_fct c

        , base_fct d

where   a.n = b.l

and     a.k = c.l

and     (a.n - a.k) = d.l

order by

    a.n

    ,a.k

 

 

 

점화식으로 구하기

 

An1 = 1

Ann = 1

Ank = A(n-1)(k-1) + A(n-1)k

 

이므로 이를 구하면

 

select

    *

from

    (

        select

            b.l n

            ,a.l k

        from    (

                    select

                        level-1 l

                    from    dual

                    connect by  level <= 10

                ) a

                , (

                    select

                        level-1 l

                    from    dual

                    connect by  level <= 10

                ) b

        where   a.l <= b.l

        order by

            n,k

    ) a

model

    DIMENSION by (n,k)

    MEASURES ( CAST(1 AS NUMBER) n_c_r )

    RULES AUTOMATIC ORDER

    (n_c_r[n,k] = case when cv(n) = 0 and cv(k) = 0 then 1 else nvl(n_c_r[cv(n)-1,cv(k)-1],0) + nvl(n_c_r[cv(n)-1,cv(k)],0) end)