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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), ...
3

%I #12 Feb 09 2015 23:48:04

%S 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 720,720,720,720,112,720,5040,5040,5040,5040,5040,5040,1008,6480,

%U 40320,40320,40320,40320,40320,40320,40320,4320,50400,362880,362880,362880,362880,362880,362880,362880,362880

%N 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 An auxiliary array for computing A088488.

%H 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 T(n,k) = n! / Product_{m=(n-floor((2n)/(3^k))) .. (n-floor((n)/(3^k)))} m.

%e The first rows of the triangular table:

%e 1

%e 1, 1

%e 3, 2, 2

%e 4, 6, 6, 6

%e 5, 6, 24, 24, 24

%e 30, 24, 120, 120, 120, 120

%e 84, 120, 720, 720, 720, 720, 720

%e 112, 720, 5040, 5040, 5040, 5040, 5040, 5040

%e 1008, 6480, 40320, 40320, 40320, 40320, 40320, 40320, 40320

%e 4320, 50400, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 362880

%e ...

%o (PARI)

%o A254876bi(n, k) = n! / prod(i=(n-((2*n)\(3^k))), (n-(n\(3^k))), i);

%o (Scheme)

%o (define (A254876 n) (A254876bi (A002024 n) (A002260 n)))

%o (define (A254876bi n k) (/ (A000142 n) (mul A000027 (- n (floor->exact (/ (* 2 n) (expt 3 k)))) (- n (floor->exact (/ n (expt 3 k)))))))

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

%Y Cf. A002024, A002260, A088488, A254864.

%K nonn,tabl

%O 1,4

%A _Antti Karttunen_, Feb 09 2015