0,3

for n>=2 a(n) = floor(n*(3-e)*n!)

a(n) = n*A056543(n)-1, n>1. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 26 2003

Comments from Peter Bala (pbala(AT)toucansurf.com), Jul 09 2008 (Start): In the following remarks we use an offset of 1, i.e. a(1) = 1, a(2) = 1, a(3) = 5, ... . For n >= 2, a(n) = n*n!*sum {k = 2..n} 1/(k*(k-1)*k!). For n >= 2, a(n) = 3*n*n! - sum {k = 0..n} (k + 1)!*C(n,k). Lim n -> infinity a(n)/(n*n!) = 3 - e. E.g.f.: 3*(1+t)/(1-t)^3 - exp(t)*(3-t)/(1-t)^3. a(n) = A083746(n+2) - A001339(n).

Recurrence relation: a(2) = 1, a(3) = 5, a(n) = (n+2)*a(n-1) - (n-1)*a(n-2) for n >=4. Recurrence relation: a(2) = 1, a(n) = (n^2*a(n-1)+1)/(n-1) for n >= 2. The recurrence relation x(n) = (n^2*x(n-1)-1)/(n-1), for n >= 2, has the general solution x(n) = n*n!*x(1) - a(n); particular solutions are A007808 (x(1) = 1) and A001339 (x(1) = 3). (End)

a:= n -> n*n!*add(1/(k*(k-1)*k!), k = 2..n): seq(a(n), n = 2..20); - Peter Bala (pbala(AT)toucansurf.com), Jul 09 2008

Cf. A074143.

Cf. A001339, A083746.

Adjacent sequences: A082422 A082423 A082424 this_sequence A082426 A082427 A082428

Sequence in context: A081924 A062512 A138772 this_sequence A109963 A091101 A134703

nonn

Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 24 2003