A232845 - OEIS

%I #22 Jun 10 2024 12:29:41

%S 0,1,0,-2,-4,-4,4,44,236,1300,8276,61484,523804,5024036,53478980,

%T 624890236,7946278604,109195935284,1612048228276,25439293045580,

%U 427278358483196,7609502950269124,143217213477235364,2840152418116021916,59189357288576068780

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

%H Robert Israel, <a href="/A232845/b232845.txt">Table of n, a(n) for n = 0..452</a>

%F a(n) ~ (n-3)!. - _Vaclav Kotesovec_, Jan 20 2014

%F E.g.f.: (1-x)^2*exp(x-1)*(Ei(1)-Ei(1-x))/2 -(1-x)^2*exp(x) - x/2 + 1. - _Robert Israel_, Jan 08 2018

%F a(n) = (-1)^(n+1)*C(n-1, 1) where C(n, x) are the Charlier polynomials (with parameter a=1) as given in A137338. (Evaluation at x = -1 gives the left factorials A003422.) - _Peter Luschny_, Nov 28 2018

%e a(8) = 6*44 - 7*4 = 236.

%p f:= gfun:-rectoproc({a(n)=(n-2)*a(n-1)-(n-1)*a(n-2),a(0)=0,a(1)=1},a(n), remember):

%p map(f, [$0..30]); # _Robert Israel_, Jan 08 2018

%p # Alternative:

%p C := proc(n, x) option remember; if n > 0 then (x-n)*C(n-1, x)-n*C(n-2, x)

%p elif n = 0 then 1 else 0 fi end: A232845 := n -> (-1)^(n+1)*C(n-1, 1):

%p seq(A232845(n), n=0..24); # _Peter Luschny_, Nov 28 2018

%t Flatten[{0,RecurrenceTable[{(-1+n) a[-2+n]+(2-n) a[-1+n]+a[n]==0, a[1]==1,a[2]==0}, a, {n, 20}]}] (* _Vaclav Kotesovec_, Jan 20 2014 *)

%t nxt[{n_,a_,b_}]:={n+1,b,b(n-1)-a*n}; NestList[nxt,{1,0,1},30][[;;,2]] (* _Harvey P. Dale_, Jun 10 2024 *)

%Y Cf. A153229, A137338, A003422.

%K sign,easy

%O 0,4

%A _Philippe Deléham_, Nov 30 2013