login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A343582 a(n) = (-1)^n*n!*[x^n] exp(-3*x)/(1 - 2*x). 1
1, 1, 5, -3, 105, -807, 10413, -143595, 2304081, -41453775, 829134549, -18240782931, 437779321785, -11382260772087, 318703306401405, -9561099177693243, 305955173729230497, -10402475906664696735, 374489132640316502949, -14230587040330864850595, 569223481613238080808201 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
The row polynomials of the rencontres numbers (A008290) evaluated at -1/2 and normalized by (-2)^n.
LINKS
FORMULA
a(n) = (-2)^n*Sum_{k=0..n} binomial(n, k)*subfactorial(n - k)*(-1/2)^k.
a(n) = 6*(n - 1)*a(n - 2) - (2*n - 3)*a(n - 1) for n >= 3.
MAPLE
egf := exp(-3*x)/(1 - 2*x): ser := series(egf, x, 32):
seq((-1)^n*n!*coeff(ser, x, n), n=0..20);
MATHEMATICA
a[n_] := (-2)^n Sum[Binomial[n, k] Subfactorial[n - k] (-2)^(-k), {k, 0, n}];
Table[a[n], {n, 0, 20}]
PROG
(Python)
def A343582():
a, b, n = 1, 5, 3
yield 1
yield a
while True:
yield b
a, b = b, 6*(n - 1)*a - (2*n - 3)*b
n += 1
a = A343582(); print([next(a) for _ in range(21)])
CROSSREFS
Sequence in context: A350213 A255599 A180403 * A267512 A230389 A048885
KEYWORD
sign
AUTHOR
Peter Luschny, Apr 24 2021
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 22 22:43 EST 2024. Contains 370265 sequences. (Running on oeis4.)