OFFSET
0,5
LINKS
Seiichi Manyama, Antidiagonals n = 0..81, flattened
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
1, 2, 5, 14, 42, ...
1, 7, 66, 715, 8398, ...
1, 30, 1144, 49742, 2340135, ...
1, 143, 22610, 3991995, 757398510, ...
1, 728, 482885, 347993910, 267058714626, ...
1, 3876, 10855425, 32018897274, 99543581789652, ...
MATHEMATICA
A[n_, k_]:= Binomial[(2*k+1)*n+2, k*n+1]/((2*k+1)*n+2); Table[A[k, n-k], {n, 0, 12}, {k, 0, n}] (* G. C. Greubel, Feb 16 2019 *)
PROG
(PARI) {A(n, k) = binomial((2*k+1)*n+2, k*n+1)/((2*k+1)*n+2)};
for(n=0, 12, for(k=0, n, print1(A(k, n-k), ", "))) \\ G. C. Greubel, Feb 16 2019
(Magma) [[Binomial((2*(n-k)+1)*k+2, k*(n-k)+1)/((2*(n-k)+1)*k+2): k in [0..n]]: n in [0..12]]; // G. C. Greubel, Feb 16 2019
(Sage) [[binomial((2*(n-k)+1)*k+2, k*(n-k)+1)/((2*(n-k)+1)*k+2) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Feb 16 2019
(GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial((2*(n-k)+1)*k+2, k*(n-k)+1)/((2*(n-k)+1)*k+2) ))); # G. C. Greubel, Feb 16 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Feb 15 2019
STATUS
approved