OFFSET
0,4
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..500
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.
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 *)
PROG
(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
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, May 01 2017
STATUS
approved