A334578 revision #36
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A334578
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Double subfactorials: a(n) = (-1)^floor(n/2) * n!! * Sum_{i=0..floor(n/2)} (-1)^i/(n-2*i)!!.
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1
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1, 1, 1, 2, 5, 11, 29, 76, 233, 685, 2329, 7534, 27949, 97943, 391285, 1469144, 6260561, 24975449, 112690097, 474533530, 2253801941, 9965204131, 49583642701, 229199695012, 1190007424825, 5729992375301, 30940193045449, 154709794133126, 866325405272573
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = n*a(n-2) + (-1)^floor(n/2).
a(2n+1)/A006882(2n+1) ~ sqrt(Pi/(2*e))*erfi(1/sqrt(2)) = A306858. (End)
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EXAMPLE
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a(5) = (5*3*1)*(1/(1) - 1/(3*1) + 1/(5*3*1)) = 15-5+1 = 11.
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MAPLE
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a:= proc(n) option remember; `if`(n<2, [0$2, 1$2][n+3],
(n-1)*a(n-2)+(n-2)*a(n-4))
end:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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proposed
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