login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 


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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 21 22:57 EDT 2024. Contains 376090 sequences. (Running on oeis4.)