OFFSET
0,5
LINKS
G. C. Greubel, Rows n = 0..30 of the triangle, flattened
FORMULA
T(n, k, m) = round( Product_{j=0..m} b(n+j, k+j)/b(n-k+j, j) ), where b(n, k) = binomial(2*n, 2*k) and m = 7.
Sum_{k=0..n} T(n, k, 7) = A151614(n).
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 153, 1;
1, 4845, 4845, 1;
1, 74613, 2362745, 74613, 1;
1, 735471, 358664691, 358664691, 735471, 1;
1, 5311735, 25533510145, 393216056233, 25533510145, 5311735, 1;
MATHEMATICA
b[n_, k_]:= Binomial[2*n, 2*k];
T[n_, k_, m_]:= Round[Product[b[n+j, k+j]/b[n-k+j, j], {j, 0, m}]];
Table[T[n, k, 7], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jun 19 2021 *)
PROG
(Magma)
A156740:= func< n, k | Round( (&*[Binomial(2*(n+j), 2*(k+j))/Binomial(2*(n-k+j), 2*j): j in [0..7]]) ) >;
[A156740(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 19 2021
(Sage)
def A156740(n, k): return round( product( binomial(2*(n+j), 2*(k+j))/binomial(2*(n-k+j), 2*j) for j in (0..7)) )
flatten([[A156740(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 19 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Feb 14 2009
EXTENSIONS
Definition corrected to give integral terms and edited by G. C. Greubel, Jun 19 2021
STATUS
approved