A007611 a(n) = n! + 2^n. (Formerly M0807)

2, 3, 6, 14, 40, 152, 784, 5168, 40576, 363392, 3629824, 39918848, 479005696, 6227028992, 87178307584, 1307674400768, 20922789953536, 355687428227072, 6402373705990144, 121645100409356288, 2432902008177688576

Offset

0,1

Comments

Answer to the problem A1 proposed during the 51th Putnam Competition in 1990 (see Kedlaya and Larson links). - Bernard Schott, Mar 29 2023

References

Ron Larson, Robert P. Hostetler and Bruce H. Edwards, Exercise 135 in Calculus of a Single Variable for Advanced High School Students, Page 605, 8th Edition, 2006.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200.

Kiran S. Kedlaya, Problem A-1, The 51th William Lowell Putnam Mathematical Competition, Dec 08 1990.

Loren Larson, Problem A-1, 51st Annual Putnam Competition, Math. Mag., 64 (1991), 141-144.

Index entries for sequences related to factorial numbers.

Index to sequences related to Olympiads and other Mathematical Competitions.

Formula

a(n) = (n+4)*a(n-1) - 4*n*a(n-2) + (4*n-8)*a(n-3) with a(0) = 2, a(1) = 3, a(2) = 6. - Dennis S. Kluk (mathemagician(AT)ameritech.net), Feb 12 2006

From Robert Israel, Mar 06 2016: (Start)

a(n) = A000079(n) + A000142(n).

E.g.f.: 1/(1-x) + exp(2x). (End)

Maple

seq(2^n+n!, n=0..50); # Robert Israel, Mar 06 2016

Mathematica

Table[n! + 2^n, {n, 0, 19}] (* Alonso del Arte, Mar 06 2016 *)

Prog

(Sage) [factorial(n)+2^n for n in range(0, 21)] # Zerinvary Lajos, Oct 27 2009
(Magma) [Factorial(n)+ 2^n: n in [0..30]]; // Vincenzo Librandi, Jun 10 2013
(PARI) a(n) = n! + 2^n; \\ Michel Marcus, Mar 30 2023

Crossrefs

Cf. A000079, A000142.

Sequence in context: A157100 A081293 A193215 * A098641 A188775 A015892

Adjacent sequences: A007608 A007609 A007610 * A007612 A007613 A007614

Keyword

nonn,easy

Author

N. J. A. Sloane, Robert G. Wilson v

Status

approved