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

Author

Antti Karttunen, Feb 09 2015

Keywords

• nonn
• tabl

Comments

An auxiliary array for computing A088488.

Examples

			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
...
		

Links

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

Crossrefs

Cf. A002024, A002260, A088488, A254864.

Programs

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)))))))

Formula

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