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%I #10 Mar 09 2021 03:03:13
%S 1,2,4,9,22,57,155,441,1311,4066,13130,44046,153144,550706,2044248,
%T 7819897,30779570,124487688,516723174,2198726181,9581247648,
%U 42717268934,194688593966,906331074605,4306472500778,20871165469241,103106015116437
%N Sums of antidiagonals of A099239.
%H G. C. Greubel, <a href="/A099241/b099241.txt">Table of n, a(n) for n = 0..500</a>
%F a(n) = Sum_{k=0..n} Sum_{j=0..n-k} binomial(k*(n-k) - (k-1)*(j-1), j).
%t A099239[n_, k_]:= Sum[Binomial[k*(n-k) -(k-1)*(j-1), j], {j,0,n-k}];
%t Table[Sum[A099239[n, k], {k,0,n}], {n,0,30}] (* _G. C. Greubel_, Mar 09 2021 *)
%o (Sage)
%o def A099239(n,k): return sum(binomial(k*(n-k)-(k-1)*(j-1), j) for j in (0..n-k))
%o [sum(A099239(n,k) for k in (0..n)) for n in (0..30)] # _G. C. Greubel_, Mar 09 2021
%o (Magma)
%o A099239:= func< n,k | (&+[Binomial(k*(n-k) -(k-1)*(j-1), j): j in [0..n-k]]) >;
%o [(&+[A099239(n,j): j in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Mar 09 2021
%Y Cf. A099239.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Oct 08 2004
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