A254864 - OEIS

%I #15 Feb 09 2015 23:47:47

%S 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,

%T 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,

%U 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

%N 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), ...

%C An auxiliary array for computing A088487.

%H Antti Karttunen, <a href="/A254864/b254864.txt">Table of n, a(n) for n = 1..10440; the first 144 rows of triangular table</a>

%F T(n,k) = n! / (n-floor(n/3^k))! = A000142(n) / A000142(n-floor(n/A000244(k))).

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

%e The first 27 rows of a triangular table:

%e 1

%e 1, 1

%e 3, 1, 1

%e 4, 1, 1, 1

%e 5, 1, 1, 1, 1

%e 30, 1, 1, 1, 1, 1

%e 42, 1, 1, 1, 1, 1, 1

%e 56, 1, 1, 1, 1, 1, 1, 1

%e 504, 9, 1, 1, 1, 1, 1, 1, 1

%e 720, 10, 1, 1, 1, 1, 1, 1, 1, 1

%e 990, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1

%e 11880, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

%e 17160, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

%e 24024, 14, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

%e 360360, 15, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

%e 524160, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

%e 742560, 17, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

%e 13366080, 306, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

%e 19535040, 342, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

%e 27907200, 380, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

%e 586051200, 420, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

%e 859541760, 462, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

%e 1235591280, 506, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

%e 29654190720, 552, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

%e 43609104000, 600, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

%e 62990928000, 650, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

%e 1700755056000, 17550, 27, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

%e ...

%e (the last ones truncated a bit).

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

%o (Scheme)

%o (define (A254864 n) (A254864bi (A002024 n) (A002260 n)))

%o ;; The above function can then use either one of these:

%o (define (A254864bi n k) (/ (A000142 n) (A000142 (- n (floor->exact (/ n (expt 3 k)))))))

%o (define (A254864bi n k) (mul A000027 (+ 1 (- n (floor->exact (/ n (expt 3 k))))) n))

%o (define (mul intfun lowlim uplim) (let multloop ((i lowlim) (res 1)) (cond ((> i uplim) res) (else (multloop (+ 1 i) (* res (intfun i)))))))

%Y The leftmost column: A254865.

%Y Cf. A000142, A000244, A088487, A254876.

%K nonn,tabl

%O 1,4

%A _Antti Karttunen_, Feb 09 2015