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A254876 Triangular table T(n,k) = n! / Product_{m=(n-floor((2n)/(3^k))) .. (n-floor((n)/(3^k)))} m, read by rows T(1,1), T(2,1), T(2,2), T(3,1), T(3,2), T(3,3), ...

%I A254876 #12 Feb 09 2015 23:48:04
%S A254876 1,1,1,3,2,2,4,6,6,6,5,6,24,24,24,30,24,120,120,120,120,84,120,720,
%T A254876 720,720,720,720,112,720,5040,5040,5040,5040,5040,5040,1008,6480,
%U A254876 40320,40320,40320,40320,40320,40320,40320,4320,50400,362880,362880,362880,362880,362880,362880,362880,362880
%N A254876 Triangular table T(n,k) = n! / Product_{m=(n-floor((2n)/(3^k))) .. (n-floor((n)/(3^k)))} m, read by rows T(1,1), T(2,1), T(2,2), T(3,1), T(3,2), T(3,3), ...
%C A254876 An auxiliary array for computing A088488.
%H A254876 Antti Karttunen, <a href="/A254876/b254876.txt">Table of n, a(n) for n = 1..1275; the first 50 rows of triangular table</a>
%F A254876 T(n,k) = n! / Product_{m=(n-floor((2n)/(3^k))) .. (n-floor((n)/(3^k)))} m.
%e A254876 The first rows of the triangular table:
%e A254876 1
%e A254876 1, 1
%e A254876 3, 2, 2
%e A254876 4, 6, 6, 6
%e A254876 5, 6, 24, 24, 24
%e A254876 30, 24, 120, 120, 120, 120
%e A254876 84, 120, 720, 720, 720, 720, 720
%e A254876 112, 720, 5040, 5040, 5040, 5040, 5040, 5040
%e A254876 1008, 6480, 40320, 40320, 40320, 40320, 40320, 40320, 40320
%e A254876 4320, 50400, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 362880
%e A254876 ...
%o A254876 (PARI)
%o A254876 A254876bi(n, k) = n! / prod(i=(n-((2*n)\(3^k))), (n-(n\(3^k))), i);
%o A254876 (Scheme)
%o A254876 (define (A254876 n) (A254876bi (A002024 n) (A002260 n)))
%o A254876 (define (A254876bi n k) (/ (A000142 n) (mul A000027 (- n (floor->exact (/ (* 2 n) (expt 3 k)))) (- n (floor->exact (/ n (expt 3 k)))))))
%o A254876 (define (mul intfun lowlim uplim) (let multloop ((i lowlim) (res 1)) (cond ((> i uplim) res) (else (multloop (+ 1 i) (* res (intfun i)))))))
%Y A254876 Cf. A002024, A002260, A088488, A254864.
%K A254876 nonn,tabl
%O A254876 1,4
%A A254876 _Antti Karttunen_, Feb 09 2015