A286032 a(n) = a(n-1) - n*a(n-2); a(0) = a(1) = 1.

1, 1, -1, -4, 0, 20, 20, -120, -280, 800, 3600, -5200, -48400, 19200, 696800, 408800, -10740000, -17689600, 175630400, 511732800, -3000875200, -13747264000, 52271990400, 368459062400, -886068707200, -10097545267200, 12940241120000, 285573963334400

Offset: 0

Author

Peter Luschny, May 01 2017

Keywords

• sign

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..500

Crossrefs

Row sums of A137286.

Programs

Maple

a := proc(n) option remember;
if n <= 1 then 1 else a(n-1) - n*a(n-2) fi end:
seq(a(n), n = 0..27);
a_list := proc(len) 1 - sqrt(Pi/2)*exp(-((x-1)^2)/2)*(x-1)*
(erfi((x-1)/sqrt(2)) + erfi(1/sqrt(2))); series(%, x, len+2):
seq(n!*simplify(coeff(%,x,n)),n=0..len-1) end: a_list(27);

Mathematica

l={1, 1}; Do[AppendTo[l, l[[-1]] - n*l[[-2]]], {n, 2, 30}]; l (* Indranil Ghosh, May 01 2017 *)
RecurrenceTable[{a[0]==a[1]==1,a[n]==a[n-1]-n a[n-2]},a,{n,40}] (* Harvey P. Dale, Jun 20 2021 *)

Python

l=[1, 1]
a=b=1
i=2
while i<=30:
    l.append(b - i*a)
    b=l[-1]
    a=l[-2]
    i+=1
print(l) # Indranil Ghosh, May 01 2017

Formula

a(n) = n! [x^n] (1 - sqrt(Pi / 2) * exp(-((x - 1)^2) / 2) * (x - 1) * (erfi((x - 1) / sqrt(2)) + erfi(1 / sqrt(2)))).

Generating function satisfies x^3*A'(x) + (2*x^2-x+1)*A(x) = 1.