OFFSET
1,3
COMMENTS
Informally: Take the upper third of natural numbers in range [1..n] and multiply them together.
LINKS
Robert Israel, Table of n, a(n) for n = 1..1025
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 (mul intfun lowlim uplim) (let multloop ((i lowlim) (res 1)) (cond ((> i uplim) res) (else (multloop (+ 1 i) (* res (intfun i)))))))
(PARI) a(n) = prod(k=1+n-n\3, n, k); \\ Michel Marcus, Jul 15 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 09 2015
STATUS
approved