OFFSET
0,5
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n, k, m) = b(n, m)/(b(k, m)*b(n-k, m)) with b(n, k) = Product_{j=1..n} ( Sum_{i=0..j-1} binomial(j-1, i)*(k+1)^i ), b(n, 0) = n!, and m = 15.
T(n, k, m) = (m+2)^(k*(n-k)) with m = 15. - G. C. Greubel, Jun 28 2021
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 17, 1;
1, 289, 289, 1;
1, 4913, 83521, 4913, 1;
1, 83521, 24137569, 24137569, 83521, 1;
1, 1419857, 6975757441, 118587876497, 6975757441, 1419857, 1;
MATHEMATICA
(* First program *)
b[n_, k_]:= b[n, k]= If[k==0, n!, Product[Sum[Binomial[j-1, i]*(k+1)^i, {i, 0, j-1}], {j, n}]];
T[n_, k_, m_]:= T[n, k, m]= b[n, m]/(b[k, m]*b[n-k, m]);
Table[T[n, k, 15], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jun 28 2021 *)
(* Second program *)
T[n_, k_, m_]:= (m+2)^(k*(n-k)); Table[T[n, k, 15], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jun 28 2021 *)
PROG
(Magma)
A156581:= func< n, k, m | (m+2)^(k*(n-k)) >;
[A156581(n, k, 15): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 28 2021
(Sage)
def A156581(n, k, m): return (m+2)^(k*(n-k))
flatten([[A156581(n, k, 15) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 28 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Feb 10 2009
EXTENSIONS
Edited by G. C. Greubel, Jun 28 2021
STATUS
approved