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A156742
Triangle T(n, k, m) = round( Product_{j=0..m} binomial(2*(n+j), 2*(k+j))/binomial( 2*(n-k+j), 2*j) ), where m = 9, read by rows.
4
1, 1, 1, 1, 231, 1, 1, 10626, 10626, 1, 1, 230230, 10590580, 230230, 1, 1, 3108105, 3097744650, 3097744650, 3108105, 1, 1, 30045015, 404255676825, 8758872997875, 404255676825, 30045015, 1, 1, 225792840, 29367745734600, 8590065627370500, 8590065627370500, 29367745734600, 225792840, 1
OFFSET
0,5
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 = 9.
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 231, 1;
1, 10626, 10626, 1;
1, 230230, 10590580, 230230, 1;
1, 3108105, 3097744650, 3097744650, 3108105, 1;
1, 30045015, 404255676825, 8758872997875, 404255676825, 30045015, 1;
MATHEMATICA
T[n_, k_, m_]:= Round[Product[Binomial[2*(n+j), 2*(k+j)]/Binomial[2*(n-k+j), 2*j], {j, 0, m}]];
Table[T[n, k, 9], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jun 19 2021 *)
PROG
(Magma)
A156742:= func< n, k | Round( (&*[Binomial(2*(n+j), 2*(k+j))/Binomial(2*(n-k+j), 2*j): j in [0..9]]) ) >;
[A156742(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 19 2021
(Sage)
def A156742(n, k): return round( product( binomial(2*(n+j), 2*(k+j))/binomial(2*(n-k+j), 2*j) for j in (0..9)) )
flatten([[A156742(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 19 2021
CROSSREFS
Cf. A086645 (m=0), A156739 (m=6), A156740 (m=7), A156741 (m=8), this sequence (m=9).
Sequence in context: A051183 A251275 A323321 * A031965 A316095 A345795
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