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A120101
Triangle T(n,k) = lcm(1,...,2*n+2)/((k+1)*binomial(2*k+2,k+1)).
7
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, 6126120, 1021020, 204204, 43758, 9724, 2210, 510, 119, 28, 116396280, 19399380, 3879876, 831402, 184756, 41990, 9690, 2261, 532, 126
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
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
First column is A119634. Second column is A051538. Main diagonal is A068553. Subdiagonal is A119636. Inverse is A120113. Row sums are A120106. Diagonal sums are A120107.
Sequence in context: A118933 A046212 A120105 * A178726 A030524 A327022
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Jun 09 2006
STATUS
approved