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A254865
a(n) = Product_{k = 1+n-floor(n/3) .. n} k.
2
1, 1, 3, 4, 5, 30, 42, 56, 504, 720, 990, 11880, 17160, 24024, 360360, 524160, 742560, 13366080, 19535040, 27907200, 586051200, 859541760, 1235591280, 29654190720, 43609104000, 62990928000, 1700755056000, 2506375872000, 3634245014400, 109027350432000, 160945136352000, 234102016512000, 7725366544896000, 11420107066368000
OFFSET
1,3
COMMENTS
Informally: Take the upper third of natural numbers in range [1..n] and multiply them together.
LINKS
FORMULA
a(n) = Product_{k = 1+n-floor(n/3) .. n} k.
Other identities. For all n >= 1:
a(3n) = A064352(n).
From Robert Israel, Jul 15 2020: (Start) a(n) = n!/(n-floor(n/3))!.
a(3*k) = 3*k*a(3*k-1).
a(3*k+1) = (3*k+1)*a(3*k)/(2*k+1).
a(3*k+2) = (3*k+2)*a(3*k+1)/(2*k+2).
E.g.f.: (cosh(x^(3/2))-1)*(1+1/x) + sinh(x^(3/2))/sqrt(x).
(End)
MAPLE
seq(n!/(n-floor(n/3))!, n=1..50); # Robert Israel, Jul 15 2020
MATHEMATICA
Array[#!/(# - Floor[#/3])! &, 34] (* Michael De Vlieger, Jul 15 2020 *)
PROG
(Scheme)
(define (A254865 n) (mul A000027 (+ 1 (- n (floor->exact (/ n 3)))) n))
(define (mul intfun lowlim uplim) (let multloop ((i lowlim) (res 1)) (cond ((> i uplim) res) (else (multloop (+ 1 i) (* res (intfun i)))))))
(define (A254865 n) (A254864bi n 1)) ;; Alternatively, using code given in A254864.
(PARI) a(n) = prod(k=1+n-n\3, n, k); \\ Michel Marcus, Jul 15 2020
CROSSREFS
Leftmost column of A254864.
Trisection: A064352.
Sequence in context: A370625 A085285 A282250 * A085841 A163483 A327876
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 09 2015
STATUS
approved