| 작성자 | 아주소설을써라써 | ||
|---|---|---|---|
| 작성일 | 2011-04-13 23:21:55 KST | 조회 | 94 |
| 제목 |
머리도 식힐 겸 해서
|
||
이거나 생각해보셈
| ||||||||||||||||||||||||||||||||||||||||||||||||
The The central trinomial coefficient is also gives the number of permutations of The generating function is given by
The central trinomial coefficients are given by the recurrence equation
with The coefficients satisfy the congruence
(T. D. Noe, pers. comm., Mar. 15, 2005) and
for Sum are given by
Closed form include
where The numbers of prime factors (with multiplicity) for   A plot of the central trinomial coefficient in the complex plane is given above. Considering instead the coefficient of
where |
|
||
|
|
||
|
© PlayXP Inc. All Rights Reserved.
디아3
th central trinomial coefficient is defined as the coefficient of 
in the expansion of 
. It is therefore the middle column of the 
. The first few central trinomial coefficients for 
, 2, ... are 1, 3, 7, 19, 51, 141, 393, ... (Sloane's 
symbols, each 
, 0, or 1, which sum to 0. For example, there are seven such permutations of three symbols: 
, 
, 
, 
, and 
, 
, 
. 
, but cannot be expressed as a fixed number of hypergeometric terms (Petkovšek et al. 1996, p. 160). 
a prime, which is easy to show using 
is a 
is a 
is a 
, 2, ... are 0, 1, 1, 1, 2, 2, 2, 4, 2, 2, 3, 2, ... (Sloane's 
is therefore prime for 
, 3, and 4, with no others for 
(E. W. Weisstein, Mar. 14, 2005). It has apparently not been proved that no prime central trinomials exist. Moreover, a more general unproven conjecture states that there are no prime trinomial coefficients except these three central trinomials and all trinomials of the form 
. 
in the expansion of 
for 
, 2, ... gives the corresponding sequence 
, 
, 5, 
, 
, 41, 
, 
, 365, 
, ... (Sloane's 
is a 
, 4, 5, 6, 7, 10, 11, 12, 26, 160, 3787, ... (Sloane's 
(E. W. Weisstein, Mar. 7, 2005). 
