cp's OEIS Frontend

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), ...

%I A254864 #15 Feb 09 2015 23:47:47
%S A254864 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 A254864 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 A254864 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 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), ...
%C A254864 An auxiliary array for computing A088487.
%H A254864 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 A254864 T(n,k) = n! / (n-floor(n/3^k))! = A000142(n) / A000142(n-floor(n/A000244(k))).
%F A254864 T(n,k) = Product_{m=1+(n-floor(n/(3^k))) .. n} m.
%e A254864 The first 27 rows of a triangular table:
%e A254864 1
%e A254864 1, 1
%e A254864 3, 1, 1
%e A254864 4, 1, 1, 1
%e A254864 5, 1, 1, 1, 1
%e A254864 30, 1, 1, 1, 1, 1
%e A254864 42, 1, 1, 1, 1, 1, 1
%e A254864 56, 1, 1, 1, 1, 1, 1, 1
%e A254864 504, 9, 1, 1, 1, 1, 1, 1, 1
%e A254864 720, 10, 1, 1, 1, 1, 1, 1, 1, 1
%e A254864 990, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A254864 11880, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A254864 17160, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A254864 24024, 14, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A254864 360360, 15, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A254864 524160, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A254864 742560, 17, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A254864 13366080, 306, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A254864 19535040, 342, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A254864 27907200, 380, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A254864 586051200, 420, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A254864 859541760, 462, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A254864 1235591280, 506, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A254864 29654190720, 552, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A254864 43609104000, 600, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A254864 62990928000, 650, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A254864 1700755056000, 17550, 27, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A254864 ...
%e A254864 (the last ones truncated a bit).
%o A254864 (PARI) A254864bi(n,k) = prod(i=(1+(n-(n\(3^k)))),n,i);
%o A254864 (Scheme)
%o A254864 (define (A254864 n) (A254864bi (A002024 n) (A002260 n)))
%o A254864 ;; The above function can then use either one of these:
%o A254864 (define (A254864bi n k) (/ (A000142 n) (A000142 (- n (floor->exact (/ n (expt 3 k)))))))
%o A254864 (define (A254864bi n k) (mul A000027 (+ 1 (- n (floor->exact (/ n (expt 3 k))))) n))
%o A254864 (define (mul intfun lowlim uplim) (let multloop ((i lowlim) (res 1)) (cond ((> i uplim) res) (else (multloop (+ 1 i) (* res (intfun i)))))))
%Y A254864 The leftmost column: A254865.
%Y A254864 Cf. A000142, A000244, A088487, A254876.
%K A254864 nonn,tabl
%O A254864 1,4
%A A254864 _Antti Karttunen_, Feb 09 2015