A254876 Triangular table T(n,k) = n! / Product_{m=(n-floor((2n)/(3^k))) .. (n-floor((n)/(3^k)))} m, read by rows T(1,1), T(2,1), T(2,2), T(3,1), T(3,2), T(3,3), ...

1, 1, 1, 3, 2, 2, 4, 6, 6, 6, 5, 6, 24, 24, 24, 30, 24, 120, 120, 120, 120, 84, 120, 720, 720, 720, 720, 720, 112, 720, 5040, 5040, 5040, 5040, 5040, 5040, 1008, 6480, 40320, 40320, 40320, 40320, 40320, 40320, 40320, 4320, 50400, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 362880

Offset

1,4

Comments

An auxiliary array for computing A088488.

Links

Antti Karttunen, Table of n, a(n) for n = 1..1275; the first 50 rows of triangular table

Formula

T(n,k) = n! / Product_{m=(n-floor((2n)/(3^k))) .. (n-floor((n)/(3^k)))} m.

Example

The first rows of the triangular table:
1
1, 1
3, 2, 2
4, 6, 6, 6
5, 6, 24, 24, 24
30, 24, 120, 120, 120, 120
84, 120, 720, 720, 720, 720, 720
112, 720, 5040, 5040, 5040, 5040, 5040, 5040
1008, 6480, 40320, 40320, 40320, 40320, 40320, 40320, 40320
4320, 50400, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 362880
...

Prog

(PARI)
A254876bi(n, k) = n! / prod(i=(n-((2*n)\(3^k))), (n-(n\(3^k))), i);
(Scheme)
(define (A254876 n) (A254876bi (A002024 n) (A002260 n)))
(define (A254876bi n k) (/ (A000142 n) (mul A000027 (- n (floor->exact (/ (* 2 n) (expt 3 k)))) (- n (floor->exact (/ n (expt 3 k)))))))
(define (mul intfun lowlim uplim) (let multloop ((i lowlim) (res 1)) (cond ((> i uplim) res) (else (multloop (+ 1 i) (* res (intfun i)))))))

Crossrefs

Cf. A002024, A002260, A088488, A254864.

Sequence in context: A245572 A344985 A325596 * A249159 A230871 A111241

Adjacent sequences: A254873 A254874 A254875 * A254877 A254878 A254879

Keyword

nonn,tabl

Author

Antti Karttunen, Feb 09 2015

Status

approved