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A129831
Alternating sum of double factorials: n!! - (n-1)!! + (n-2)!! - ... 1!!.
2
1, 1, 2, 6, 9, 39, 66, 318, 627, 3213, 7182, 38898, 96237, 548883, 1478142, 8843778, 25615647, 160178913, 494550162, 3221341038, 10527969537, 71221636863, 245012506362, 1716978047238, 6188875533387, 44822878860213
OFFSET
1,3
FORMULA
a(n) = n!! - (n-1)!! + (n-2)!! - ... 1!! = A006882(n) - a(n-1).
EXAMPLE
a(5) = 5!! - 4!! + 3!! - 2!! + 1!! = 15 - 8 + 3 - 2 + 1 = 9.
MAPLE
A129831 := proc(n)
add( (-1)^i*doublefactorial(n-i), i=0..n-1) ;
end proc: # R. J. Mathar, Aug 22 2012
CROSSREFS
Sequence in context: A093397 A332066 A082459 * A101713 A240761 A342317
KEYWORD
nonn
AUTHOR
STATUS
approved