OFFSET
0,2
COMMENTS
The rows give the coefficients of polynomials arising in the integration of x^(2m)/sqrt(4-x^2), m >= 0.
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..5050
FORMULA
Number triangle T(n,k) = [k<=n] * lcm(1,...,2n+2)/((k+1)*binomial(2k+2, k+1)).
EXAMPLE
Triangle begins:
1;
6, 1;
30, 5, 1;
420, 70, 14, 3;
1260, 210, 42, 9, 2;
13860, 2310, 462, 99, 22, 5;
180180, 30030, 6006, 1287, 286, 65, 15;
360360, 60060, 12012, 2574, 572, 130, 30, 7;
MAPLE
T:=(n, k)-> ilcm(seq(q, q=1..2*n+2))/((k+1)*binomial(2*k+2, k+1)): seq(seq(T(n, k), k=0..n), n=0..9); # Muniru A Asiru, Feb 26 2019
MATHEMATICA
Table[LCM@@Range[2*n+2]/((k+1)*Binomial[2*k+2, k+1]), {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, May 03 2023 *)
PROG
(GAP) Flat(List([0..9], n->List([0..n], k->Lcm(List([1..2*n+2], i->i))/((k+1)*Binomial(2*k+2, k+1))))); # Muniru A Asiru, Feb 26 2019
(Magma) [Lcm([1..2*n+2])/((k+1)*(k+2)*Catalan(k+1)): k in [0..n], n in [0..12]]; // G. C. Greubel, May 03 2023
(SageMath)
def A120101(n, k):
return lcm(range(1, 2*n+3))/((k+1)*(k+2)*catalan_number(k+1))
flatten([[A120101(n, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, May 03 2023
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Jun 09 2006
STATUS
approved