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A007911 (n-1)!!-(n-2)!!. 5
1, 1, 5, 7, 33, 57, 279, 561, 2895, 6555, 35685, 89055, 509985, 1381905, 8294895, 24137505, 151335135, 468934515, 3061162125, 10033419375, 68000295825, 234484536825, 1645756410375, 5943863027025, 43105900812975 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,3

COMMENTS

For n >= 0 let A(n) 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

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]

CROSSREFS

Cf. A007912.

Sequence in context: A104815 A230997 A243019 * A066172 A175667 A018353

Adjacent sequences:  A007908 A007909 A007910 * A007912 A007913 A007914

KEYWORD

nonn,easy

AUTHOR

J. H. Conway

STATUS

approved

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Last modified July 21 17:51 EDT 2017. Contains 289643 sequences.