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

0,2

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

Cf. A099239.

Sequence in context: A196161 A333069 A249561 * A337067 A249563 A124380

Adjacent sequences: A099238 A099239 A099240 * A099242 A099243 A099244

Keyword

easy,nonn

Author

Paul Barry, Oct 08 2004

Status

approved