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

1,4

Comments

An auxiliary array for computing A088487.

Links

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

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.

Example

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).

Prog

(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)))))))

Crossrefs

The leftmost column: A254865.

Cf. A000142, A000244, A088487, A254876.

Sequence in context: A177058 A176921 A000503 * A111956 A024564 A084795

Adjacent sequences: A254861 A254862 A254863 * A254865 A254866 A254867

Keyword

nonn,tabl

Author

Antti Karttunen, Feb 09 2015

Status

approved