OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
FORMULA
a(n) = Sum_{k=0..n} Sum_{j=0..n-k} binomial(k*(n-k) - (k-1)*(j-1), j).
MATHEMATICA
A099239[n_, k_]:= Sum[Binomial[k*(n-k) -(k-1)*(j-1), j], {j, 0, n-k}];
Table[Sum[A099239[n, k], {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, Mar 09 2021 *)
PROG
(Sage)
def A099239(n, k): return sum(binomial(k*(n-k)-(k-1)*(j-1), j) for j in (0..n-k))
[sum(A099239(n, k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Mar 09 2021
(Magma)
A099239:= func< n, k | (&+[Binomial(k*(n-k) -(k-1)*(j-1), j): j in [0..n-k]]) >;
[(&+[A099239(n, j): j in [0..n]]): n in [0..30]]; // G. C. Greubel, Mar 09 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 08 2004
STATUS
approved