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A185109
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a(0)=2; for n > 0, a(n) = (n+2)*a(n-1) + 1.
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4
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2, 7, 29, 146, 877, 6140, 49121, 442090, 4420901, 48629912, 583558945, 7586266286, 106207728005, 1593115920076, 25489854721217, 433327530260690, 7799895544692421, 148198015349156000, 2963960306983120001, 62243166446645520022
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = e*Gamma(n+3,1)-(3/2)*(n+2)!, where Gamma(a,x) is the incomplete gamma function. [Bruno Berselli, Dec 24 2012]
a(n) ~ (exp(1)-3/2)*sqrt(2*Pi)*exp(-n)*n^(n+5/2). - Vaclav Kotesovec, Aug 13 2013
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MATHEMATICA
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RecurrenceTable[{a[0]==2, a[n]==(n+2)*a[n-1] + 1}, a, {n, 20}] (* Vincenzo Librandi, Dec 23 2012 *)
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PROG
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(Magma) [n le 1 select 2 else (n+1)*Self(n-1)+1: n in [1..20]]; // Vincenzo Librandi, Dec 22 2012
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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