A291856 - OEIS

%I #17 Sep 09 2017 21:43:22

%S -1,1,0,2,2,10,20,80,220,860,2840,11440,42680,179960,734800,3254240,

%T 14276240,66344080,309040160,1503233600,7374996640,37439668640,

%U 192314598080,1015987308160,5439223064000,29822918459840,165803495059840,941199375015680

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

%H Seiichi Manyama, <a href="/A291856/b291856.txt">Table of n, a(n) for n = 0..800</a>

%F a(n+4) = 2*A249059(n) for n >= 0.

%F E.g.f.: exp(x*(2+x)/2) * (exp(1/2) * sqrt(2*Pi) * (erf((1+x)/sqrt(2)) - erf(1/sqrt(2))) - 1). - _Vaclav Kotesovec_, Sep 05 2017

%F a(n) ~ (sqrt(Pi) * exp(1/2) * (1 - erf(1/sqrt(2))) - sqrt(2)/2) * n^(n/2) * exp(sqrt(n) - n/2 - 1/4). - _Vaclav Kotesovec_, Sep 05 2017

%t RecurrenceTable[{a[0] == -1, a[1] == 1, a[n] == a[n-1] + (n-1)*a[n-2]}, a[n], {n, 0, 20}] (* _Vaclav Kotesovec_, Sep 04 2017 *)

%t CoefficientList[Series[E^(x*(2 + x)/2) * (E^(1/2)*Sqrt[2*Pi]*(Erf[(1 + x)/Sqrt[2]] - Erf[1/Sqrt[2]]) - 1), {x, 0, 20}], x]*Range[0, 20]! (* _Vaclav Kotesovec_, Sep 05 2017 *)

%o (GAP)

%o a:=[-1,1];; for n in [3..10^2] do a[n]:=a[n-1]+(n-2)*a[n-2]; od; a;  # _Muniru A Asiru_, Sep 07 2017

%Y Cf. A000085, A000932, A249059.

%K sign

%O 0,4

%A _Seiichi Manyama_, Sep 04 2017