OFFSET
0,2
COMMENTS
Denominator of a(n)/n! is listed in A096620.
a(n) - (n+1)*a(n-1) = A129326(n), n > 0. - Gary Detlefs, Oct 04 2011
LINKS
Robert Israel, Table of n, a(n) for n = 0..448
FORMULA
From Robert Israel, Mar 28 2018: (Start)
E.g.f.: (1+x - 2*log(1-x))/(1-x)^2.
a(n+3) = (3*n+8)*a(n+2) - (3*n+7)*(n+2)*a(n+1) + (n+1)*(n+2)^2*a(n). (End)
MAPLE
H:= n-> sum(1/k, k=1..n):seq((n+1)!*(H(n+1)+H(n)), n=0..20);
# Alternative:
f:= gfun:-rectoproc({a(n+3) = (3*n+8)*a(n+2)-(3*n+7)*(n+2)*a(n+1)+(n+1)*(n+2)^2*a(n), a(0)=1, a(1)=5, a(2)=20}, a(n), remember):
map(f, [$0..50]); # Robert Israel, Mar 28 2018
MATHEMATICA
Table[(n+1)!Total[HarmonicNumber[{n, n+1}]], {n, 0, 20}] (* Harvey P. Dale, Jul 17 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary Detlefs, Oct 03 2011
STATUS
approved