OFFSET
0,5
COMMENTS
Row sums are the central trinomial coefficients A002426.
Coefficient array for polynomials P(n,x) = x^n*F(1/2-n/2,-n/2;1;4/x). - Paul Barry, Oct 04 2008
Column sums give A001850. It appears that the sums along the antidiagonals of the triangle produce A182883. - Peter Bala, Mar 06 2013
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows
FORMULA
G.f.: 1/(sqrt((1-x*y)^2-4*x^2*y)). - Vladimir Kruchinin, Oct 28 2020
EXAMPLE
Triangle begins
1;
0, 1;
0, 2, 1;
0, 0, 6, 1;
0, 0, 6, 12, 1;
0, 0, 0, 30, 20, 1;
MAPLE
gf := 1/((1 - x*y)^2 - 4*y^2*x)^(1/2):
yser := series(gf, y, 12): ycoeff := n -> coeff(yser, y, n):
row := n -> seq(coeff(expand(ycoeff(n)), x, k), k=0..n):
seq(row(n), n=0..7); # Peter Luschny, Oct 28 2020
MATHEMATICA
Flatten[Table[Binomial[n, k]Binomial[k, n-k], {n, 0, 20}, {k, 0, n}]] (* Harvey P. Dale, Nov 12 2014 *)
PROG
(Magma) [[Binomial(n, k)*Binomial(k, n-k): k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Jun 14 2015
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Apr 23 2005
STATUS
approved