A254864 Triangular table T(n,k) = n! / (n-floor(n/3^k))!, 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, 1, 1, 4, 1, 1, 1, 5, 1, 1, 1, 1, 30, 1, 1, 1, 1, 1, 42, 1, 1, 1, 1, 1, 1, 56, 1, 1, 1, 1, 1, 1, 1, 504, 9, 1, 1, 1, 1, 1, 1, 1, 720, 10, 1, 1, 1, 1, 1, 1, 1, 1, 990, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11880, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17160, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 24024, 14, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Feb 09 2015

Keywords

• nonn
• tabl

Comments

An auxiliary array for computing A088487.

Examples

			The first 27 rows of a triangular table:
1
1, 1
3, 1, 1
4, 1, 1, 1
5, 1, 1, 1, 1
30, 1, 1, 1, 1, 1
42, 1, 1, 1, 1, 1, 1
56, 1, 1, 1, 1, 1, 1, 1
504, 9, 1, 1, 1, 1, 1, 1, 1
720, 10, 1, 1, 1, 1, 1, 1, 1, 1
990, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1
11880, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
17160, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
24024, 14, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
360360, 15, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
524160, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
742560, 17, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
13366080, 306, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
19535040, 342, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
27907200, 380, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
586051200, 420, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
859541760, 462, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
1235591280, 506, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
29654190720, 552, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
43609104000, 600, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
62990928000, 650, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1700755056000, 17550, 27, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
...
(the last ones truncated a bit).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 rows of triangular table

Crossrefs

The leftmost column: A254865.

Cf. A000142, A000244, A088487, A254876.

Programs

PARI

A254864bi(n,k) = prod(i=(1+(n-(n\(3^k)))),n,i);

Scheme

(define (A254864 n) (A254864bi (A002024 n) (A002260 n)))
;; The above function can then use either one of these:
(define (A254864bi n k) (/ (A000142 n) (A000142 (- n (floor->exact (/ n (expt 3 k)))))))
(define (A254864bi n k) (mul A000027 (+ 1 (- n (floor->exact (/ n (expt 3 k))))) n))
(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! / (n-floor(n/3^k))! = A000142(n) / A000142(n-floor(n/A000244(k))).

T(n,k) = Product_{m=1+(n-floor(n/(3^k))) .. n} m.