A127986 a(n) = n! + 2^n - 1.

1, 2, 5, 13, 39, 151, 783, 5167, 40575, 363391, 3629823, 39918847, 479005695, 6227028991, 87178307583, 1307674400767, 20922789953535, 355687428227071, 6402373705990143, 121645100409356287, 2432902008177688575, 51090942171711537151, 1124000727777611874303

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..450 (first 250 terms from G. C. Greubel)

Florian Luca, Igor E. Shparlinsky, On the largest prime factor of n! + 2^n - 1, J. Th. des Nombres de Bordeaux 2005, Vol.17, Fasc. 3.

Formula

a(n) = n! + 2^n - 1.

a(n) = A000142(n) + A000225(n). - Wesley Ivan Hurt, Oct 23 2014

E.g.f.: 1/(1-x) + exp(2*x) - exp(x). - Alois P. Heinz, May 09 2018

Maple

A127986:=n->n!+2^n-1: seq(A127986(n), n=0..20); # Wesley Ivan Hurt, Oct 23 2014

Mathematica

Table[n! + 2^n - 1, {n, 30}] (* Artur Jasinski *)

Prog

(Sage) [gaussian_binomial(n, 1, 2)+factorial(n) for n in range(1, 21)] # Zerinvary Lajos, May 29 2009
(PARI) a(n)=n!+2^n-1 \\ Charles R Greathouse IV, Feb 01 2013
(Magma) [Factorial(n)+2^n-1 : n in [1..20]]; // Wesley Ivan Hurt, Oct 23 2014

Crossrefs

Cf. A000142, A000225, A127987.

Sequence in context: A149861 A148305 A104447 * A255600 A320809 A287967

Adjacent sequences: A127983 A127984 A127985 * A127987 A127988 A127989

Keyword

nonn,easy

Author

Artur Jasinski, Feb 09 2007

Extensions

a(0)=1 prepended by Alois P. Heinz, May 09 2018

Status

approved