OFFSET
1,2
COMMENTS
Sums of the antidiagonals of A099238. - Paul Barry, Oct 08 2004
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000 (correcting an earlier b-file from Vincenzo Librandi)
FORMULA
G.f.: Sum_{k>=1} x^k/(1-x-x^k).
a(n) = Sum_{r=0..n-1} Sum_{k=0..floor((n-r-1)/(r+1))} binomial(n-r(k+1)-1, k). - Paul Barry, Oct 08 2004
G.f.: (1-x)^2 * Sum_{k>=1} k*x^k/((x^k+x-1)*(x^(k+1)+x-1)). - Vladeta Jovovic, Apr 23 2006
G.f.: Sum_{k>=1} x^k/((1-x)^k*(1-x^k)). - Vladeta Jovovic, Mar 02 2008
G.f.: Sum_{n>=1} a*x^n/(1-a*x^n) (generalized Lambert series) where a=1/(1-x). - Joerg Arndt, Jan 30 2011
G.f.: Sum_{n>=1} (a*x)^n/(1-x^n) where a=1/(1-x). - Joerg Arndt, Jan 01 2013
G.f.: Sum_{n>=1} x^n * Sum_{d|n} 1/(1-x)^d. - Paul D. Hanna, Jul 18 2013
a(n) ~ 2^(n-1). - Vaclav Kotesovec, Oct 28 2014
MAPLE
A097939:=n->add(add(binomial(n-r*(k+1)-1, k), k=0..floor((n-r-1)/(r+1))), r=0..n-1): seq(A097939(n), n=1..50); # Wesley Ivan Hurt, Dec 03 2016
# second Maple Program:
b:= proc(n, m) option remember; `if`(n=0, m,
add(b(n-j, min(j, m)), j=1..n))
end:
a:= n-> b(n$2):
seq(a(n), n=1..40); # Alois P. Heinz, Jul 26 2020
MATHEMATICA
Drop[ CoefficientList[ Series[ Sum[x^k/(1 - x - x^k), {k, 50}], {x, 0, 35}], x], 1] (* Robert G. Wilson v, Sep 08 2004 *)
PROG
(PARI)
N=66; x='x+O('x^N);
gf= sum(k=1, N, x^k/(1-x-x^k) );
Vec(gf)
/* Joerg Arndt, Jan 01 2013 */
(PARI) {a(n)=polcoeff(sum(m=1, n, x^m*sumdiv(m, d, 1/(1-x +x*O(x^n))^d) ), n)}
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Sep 05 2004
EXTENSIONS
More terms from Robert G. Wilson v, Sep 08 2004
STATUS
approved