A185109 - OEIS

%I #17 Feb 01 2024 15:45:12

%S 2,7,29,146,877,6140,49121,442090,4420901,48629912,583558945,

%T 7586266286,106207728005,1593115920076,25489854721217,433327530260690,

%U 7799895544692421,148198015349156000,2963960306983120001,62243166446645520022

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

%H Vincenzo Librandi, <a href="/A185109/b185109.txt">Table of n, a(n) for n = 0..200</a>

%H Jia Huang and Erkko Lehtonen, <a href="https://arxiv.org/abs/2401.15786">Associative-commutative spectra for some varieties of groupoids</a>, arXiv:2401.15786 [math.CO], 2024. See p. 10.

%F 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]

%F a(n) = (n+3)*a(n-1) - (n+1)*a(n-2). - _Vaclav Kotesovec_, Aug 13 2013

%F a(n) ~ (exp(1)-3/2)*sqrt(2*Pi)*exp(-n)*n^(n+5/2). - _Vaclav Kotesovec_, Aug 13 2013

%t RecurrenceTable[{a[0]==2, a[n]==(n+2)*a[n-1] + 1}, a, {n, 20}] (* _Vincenzo Librandi_, Dec 23 2012 *)

%o (Magma) [n le 1 select 2 else (n+1)*Self(n-1)+1: n in [1..20]]; // _Vincenzo Librandi_, Dec 22 2012

%K nonn

%O 0,1

%A _Olivier Gérard_, Nov 02 2012

%E Edited by _Vincenzo Librandi_ and _N. J. A. Sloane_, Dec 24 2012