OFFSET
-1,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Robert Israel, Table of n, a(n) for n = -1..403
Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]
Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.
FORMULA
From Robert Israel, Dec 29 2015: (Start)
E.g.f. (without the n = -1 term): e^x + 1/(1 - 2*x) - e^(x - 1/2)*(Ei(1/2 - x)-Ei(1/2))/2.
a(n+2) = (2*n + 5)*a(n+1) - (2*n + 4)*a(n). (End)
MAPLE
seq(1+add(2^k*k!, k=0..n), n=-1..30); # Robert Israel, Dec 29 2015
MATHEMATICA
Join[{1}, Table[Sum[2^k k!, {k, 0, n}], {n, 0, 30}]+1] (* Harvey P. Dale, Jun 22 2022 *)
PROG
(PARI) a(n) = 1 + sum(k=0, n, 2^k*k!); \\ Michel Marcus, Dec 30 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Typo in name corrected by Sean A. Irvine, Dec 29 2015
STATUS
approved