login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 31 10:42 EDT 2020. Contains 334748 sequences. (Running on oeis4.)