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A110149
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a(0) = 1, a(1) = 3; for n>1, a(n) = n*a(n-1) + (-1)^n.
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2
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1, 3, 7, 20, 81, 404, 2425, 16974, 135793, 1222136, 12221361, 134434970, 1613219641, 20971855332, 293605974649, 4404089619734, 70465433915745, 1197912376567664, 21562422778217953, 409686032786141106, 8193720655722822121, 172068133770179264540
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OFFSET
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0,2
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COMMENTS
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A000166, A001120 and A110043 have a similar recurrence.
a(n) = (n-1)*(a(n-1)+a(n-2)), n>2. - Gary Detlefs, Apr 11 2010
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..450
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FORMULA
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a(n) = A110043(n) + n! = A001120(n) + 2*n! = A000166(n) + 3*n! for n>0.
a(n) = 3*n! + floor((n!+1)/e) for n>0. - Gary Detlefs, Apr 11 2010
E.g.f.: (3*exp(x)*x+1)*exp(-x)/(1-x). - Alois P. Heinz, May 07 2020
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MAPLE
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a:= proc(n) option remember;
`if`(n<2, 2*n+1, n*a(n-1)+(-1)^n)
end:
seq(a(n), n=0..23); # Alois P. Heinz, May 07 2020
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MATHEMATICA
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RecurrenceTable[{a[1]==3, a[n]==n a[n-1]+(-1)^n}, a, {n, 20}] (* Harvey P. Dale, Nov 21 2011 *)
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CROSSREFS
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Column k=3 of A334715.
Sequence in context: A071688 A232687 A211602 * A024331 A007174 A091184
Adjacent sequences: A110146 A110147 A110148 * A110150 A110151 A110152
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KEYWORD
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nonn,easy
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AUTHOR
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Philippe Deléham, Sep 04 2005
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EXTENSIONS
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a(0)=1 prepended by Alois P. Heinz, May 07 2020
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STATUS
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approved
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