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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), ... 4
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
An auxiliary array for computing A088487.
LINKS
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.
Sequence in context: A177058 A176921 A000503 * A111956 A024564 A084795
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Feb 09 2015
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)