A099241 Sums of antidiagonals of A099239.

1, 2, 4, 9, 22, 57, 155, 441, 1311, 4066, 13130, 44046, 153144, 550706, 2044248, 7819897, 30779570, 124487688, 516723174, 2198726181, 9581247648, 42717268934, 194688593966, 906331074605, 4306472500778, 20871165469241, 103106015116437

Offset: 0

Author

Paul Barry, Oct 08 2004

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A099239.

Programs

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

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 *)

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

Formula

a(n) = Sum_{k=0..n} Sum_{j=0..n-k} binomial(k*(n-k) - (k-1)*(j-1), j).