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A004400 a(n) = 1 + Sum_{k=0..n} 2^k*k!.
(Formerly M1263)
4
1, 2, 4, 12, 60, 444, 4284, 50364, 695484, 11017404, 196811964, 3912703164, 85662309564, 2047652863164, 53059407256764, 1481388530277564, 44331262220901564, 1415527220320869564, 48036189795719781564, 1726380042510080613564, 65503446445655792229564, 2616586102571484256869564 (list; graph; refs; listen; history; text; internal format)
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

Guo-Niu Han, Enumeration of Standard Puzzles [Cached copy]

FORMULA

From Robert Israel, Dec 29 2015: (Start)

E.g.f. (without 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

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

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Last modified October 14 17:27 EDT 2019. Contains 328022 sequences. (Running on oeis4.)