OFFSET
0,8
COMMENTS
A variant of A142589.
LINKS
G. C. Greubel, Antidiagonal rows n = 0..100, flattened
FORMULA
A(n, k) = (-n)^k*FallingFactorial(-1/n, k) for n >= 1. - Peter Luschny, Dec 21 2021
EXAMPLE
1 1 1 1 1 1 1... A000012
1 1 2 6 24 120 720... A000142
1 1 3 15 105 945 10395... A001147
1 1 4 28 280 3640 58240... A007559
1 1 5 45 585 9945 208845... A007696
1 1 6 66 1056 22176 576576... A008548
1 1 7 91 1729 43225 1339975... A008542
1 1 8 120 2640 76560 2756160... A045754
1 1 9 153 3825 126225 5175225... A045755
1 1 10 190 5320 196840 9054640... A045756
1 1 11 231 7161 293601 14977651... A144773
MAPLE
seq(seq( mul(j*k+1, j=0..n-k-1), k=0..n), n=0..12); # G. C. Greubel, Mar 04 2020
MATHEMATICA
T[n_, k_]= Product[j*k+1, {j, 0, n-1}]; Table[T[n-k, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Mar 04 2020 *)
PROG
(PARI) T(n, k) = prod(j=0, n-1, j*k+1);
for(n=0, 12, for(k=0, n, print1(T(n-k, k), ", "))) \\ G. C. Greubel, Mar 04 2020
(Magma)
function T(n, k)
if k eq 0 or n eq 0 then return 1;
else return (&*[j*k+1: j in [0..n-1]]);
end if; return T; end function;
[T(n-k, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 04 2020
(Sage) [[ product(j*k+1 for j in (0..n-k-1)) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Mar 04 2020
(GAP) Flat(List([0..12], n-> List([0..n], k-> Product([0..n-k-1], j-> j*k+1) ))); # G. C. Greubel, Mar 04 2020
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Jun 01 2015
STATUS
approved