OFFSET
3,3
COMMENTS
For n >= 0 let A(n) be the product of the positive integers <= n that have the same parity as n minus the product of the positive integers <= n that have the opposite parity as n. Then a(n) = A(n-1) (for n >= 3). [Peter Luschny, Jul 06 2011]
REFERENCES
S. P. Hurd and J. S. McCranie, Quantum factorials. Proceedings of the Twenty-fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1994). Congr. Numer. 104 (1994), 19-24.
LINKS
T. D. Noe, Table of n, a(n) for n = 3..100
FORMULA
(n-1)*a(n+2) = a(n+1) + n^2*a(n). - Robert Israel, Aug 08 2017
MAPLE
P:=proc(n) local i, j, k, w; for i from 1 by 1 to n do k:=i; w:=i-2; while w>0 do k:=k*w; w:=w-2; od; j:=i+1; w:=i-1; while w>0 do j:=j*w; w:=w-2; od; print(j-k); od; end: P(100); # Paolo P. Lava, Jun 14 2007
DDF := proc(n) local R, P, k; R := {$1..n}; P := select(k->k mod 2 = n mod 2, R); mul(k, k = P) - mul(k, k = R minus P) end: A007911 := n -> DDF(n-1); # Peter Luschny, Jul 06 2011
f:= gfun:-rectoproc({(-n+1)*a(2+n)+a(1+n)+n^2*a(n), a(2)=0, a(3)=1}, a(n), remember):
map(f, [$3..100]); # Robert Israel, Aug 08 2017
MATHEMATICA
Table[(n - 1)!! - (n - 2)!!, {n, 3, 30}] (* Vincenzo Librandi, Aug 08 2017 *)
PROG
(MAGMA) DoubleFactorial:=func< n | &*[n..2 by -2] >; [DoubleFactorial((n-1))-DoubleFactorial(n-2): n in [3..30]]; // Vincenzo Librandi, Aug 08 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
proposed