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 A185308 a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + n*a(n-2) + 1. 5

%I

%S 0,0,1,2,7,18,61,188,677,2370,9141,35212,144905,602662,2631333,

%T 11671264,53772593,252184082,1220090757,6011588316,30413403457,

%U 156656758094,825751634149,4428857070312,24246896289889,134968323047690,765387626584805,4409532348872436

%N a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + n*a(n-2) + 1.

%H Vincenzo Librandi, <a href="/A185308/b185308.txt">Table of n, a(n) for n = 0..200</a>

%F a(0)=a(1)=0, a(2)=1, a(n) = 2*a(n-1)+(n-1)*a(n-2)-(n-1)*a(n-3). - _Vincenzo Librandi_, Dec 24 2012

%F a(n) ~ (sqrt(Pi)-sqrt(2))/2 * n^(n/2+1/2)*exp(sqrt(n)-n/2-1/4) * (1+19/(24*sqrt(n))). - _Vaclav Kotesovec_, Dec 26 2012

%F E.g.f.: 1/2*exp(x)*(exp(x^2/2)*(x+1)*(sqrt(2*Pi)*erf(x/sqrt(2))-2)+2). - _Vaclav Kotesovec_, Dec 27 2012

%t RecurrenceTable[{a[0] == 0, a[1] == 0, a[n] == a[n - 1] + n a[n - 2] + 1}, a, {n, 0, 30}] (* _Bruno Berselli_, Dec 24 2012 *)

%t FullSimplify[CoefficientList[Series[1/2*E^x*(E^(x^2/2)*(x+1)*(Sqrt[2*Pi]*Erf[x/Sqrt[2]]-2)+2), {x, 0, 20}], x]* Range[0, 20]!] (* _Vaclav Kotesovec_, Dec 27 2012 *)

%o (MAGMA) I:=[0,0,1,2]; [n le 4 select I[n] else 2*Self(n-1)+(n-2)*Self(n-2)-(n-2)*Self(n-3): n in [1..30]]; _Vincenzo Librandi_, Dec 24 2012

%K nonn

%O 0,4

%A _Olivier GĂ©rard_, Nov 02 2012

%E More terms from _Vincenzo Librandi_, Dec 24 2012

%E Edited by _Bruno Berselli_, Dec 24 2012

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Last modified June 23 02:28 EDT 2021. Contains 345395 sequences. (Running on oeis4.)