A142589 Square array T(n,m) = Product_{i=0..m} (1+n*i) read by antidiagonals.
1, 1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 24, 15, 4, 1, 1, 120, 105, 28, 5, 1, 1, 720, 945, 280, 45, 6, 1, 1, 5040, 10395, 3640, 585, 66, 7, 1, 1, 40320, 135135, 58240, 9945, 1056, 91, 8, 1, 1, 362880, 2027025, 1106560, 208845, 22176, 1729, 120, 9, 1, 1, 3628800, 34459425, 24344320, 5221125, 576576, 43225, 2640, 153, 10, 1
Offset: 0
Examples
The transpose of the array is:
1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 2, 3, 4, 5, 6, 7, 8, 9,
1, 6, 15, 28, 45, 66, 91, 120, 153, ... A000384
1, 24, 105, 280, 585, 1056, 1729, 2640, 3825, ... A011199
1, 120, 945, 3640, 9945, 22176, 43225, 76560, 126225,... A011245
1, 720, 10395, 58240, 208845, 576576, 1339975, 2756160,...
/ | \ \
A000142 A001147 A007559 A007696
Links
- G. C. Greubel, Antidiagonal rows n = 0..100, flattened
Crossrefs
Programs
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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]]); end if; return T; end function; [T(n-k,k): k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 05 2020
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Maple
T:= (n, k)-> `if`(n=0, 1, mul(j*k+1, j=0..n)): seq(seq(T(n-k, k), k=0..n), n=0..12); # G. C. Greubel, Mar 05 2020
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Mathematica
T[n_, k_]= If[n==0, 1, Product[1 + k*i, {i,0,n}]]; Table[T[n-k, k], {n,0,10}, {k,0,n}]//Flatten -
PARI
T(n, k) = if(n==0, 1, prod(j=0, n, j*k+1) ); for(n=0, 12, for(k=0, n, print1(T(n-k, k), ", "))) \\ G. C. Greubel, Mar 05 2020
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Sage
def T(n, k): if (k==0 and n==0): return 1 else: return product(j*k+1 for j in (0..n)) [[T(n-k, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Mar 05 2020
Extensions
Edited by M. F. Hasler, Oct 28 2014
More terms added by G. C. Greubel, Mar 05 2020
Comments