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A110043 a(0) = 1, a(1) = 2; for n>1, a(n) = n*a(n-1) + (-1)^n. 3
1, 2, 5, 14, 57, 284, 1705, 11934, 95473, 859256, 8592561, 94518170, 1134218041, 14744834532, 206427683449, 3096415251734, 49542644027745, 842224948471664, 15160049072489953, 288040932377309106, 5760818647546182121, 120977191598469824540, 2661498215166336139881 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A000166 and A001120 have a similar recurrence.

a(n) = (n-1)*(a(n-1)+a(n-2)), n>2. - Gary Detlefs, Apr 11 2010

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

FORMULA

a(n) = A001120(n) + n! = A000166(n) + 2*n! for n>0.

a(n) = 2*n! + floor((n!+1)/e) for n>0. - Gary Detlefs, Apr 11 2010

E.g.f.: (2*exp(x)*x+1)*exp(-x)/(1-x). - Alois P. Heinz, May 07 2020

MAPLE

a:= proc(n) option remember;

      `if`(n<2, n+1, n*a(n-1)+(-1)^n)

    end:

seq(a(n), n=0..23);  # Alois P. Heinz, May 07 2020

CROSSREFS

Cf. A000142, A000166, A001120.

Column k=2 of A334715.

Sequence in context: A047042 A174795 A243551 * A006847 A008286 A049082

Adjacent sequences:  A110040 A110041 A110042 * A110044 A110045 A110046

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Sep 04 2005

EXTENSIONS

a(0)=1 prepended and two terms corrected by Alois P. Heinz, May 07 2020

STATUS

approved

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Last modified July 6 23:01 EDT 2020. Contains 335484 sequences. (Running on oeis4.)