A004400 a(n) = 1 + Sum_{k=0..n} 2^k*k!. (Formerly M1263)

1, 2, 4, 12, 60, 444, 4284, 50364, 695484, 11017404, 196811964, 3912703164, 85662309564, 2047652863164, 53059407256764, 1481388530277564, 44331262220901564, 1415527220320869564, 48036189795719781564, 1726380042510080613564, 65503446445655792229564, 2616586102571484256869564

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

Cf. A000165, A112368, A112369.

Sequence in context: A326861 A013202 A253832 * A005831 A136512 A137160

Adjacent sequences: A004397 A004398 A004399 * A004401 A004402 A004403

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Typo in name corrected by Sean A. Irvine, Dec 29 2015

Status

approved