OFFSET
0,3
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = a(n-1) + A055881(n).
a(n) = (e-1)*n + f(n) where f(n) < 0. - Benoit Cloitre, Jun 19 2002
f is unbounded in the negative direction. The assertion that f(n) < 0 is correct, since (e-1)*n = Sum_{k>=1} n/k! is term for term >= this sequence. - Franklin T. Adams-Watters, Nov 03 2005
G.f.: (1/(1 - x)) * Sum_{k>=1} x^(k!)/(1 - x^(k!)). - Ilya Gutkovskiy, Jul 11 2019
PROG
(PARI) a(n)={my(s=0, d=1, f=1); while (n>=d, s+=n\d; f++; d*=f); s} \\ Harry J. Smith, Jul 12 2009
(Magma) [0] cat [&+[Floor(m/Factorial(k)):k in [1..m]]:m in [1..70]]; // Marius A. Burtea, Jul 11 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, May 01 2001
STATUS
approved