

A105868


Triangle read by rows, T(n,k) = C(n,k)*C(k,nk).


5



1, 0, 1, 0, 2, 1, 0, 0, 6, 1, 0, 0, 6, 12, 1, 0, 0, 0, 30, 20, 1, 0, 0, 0, 20, 90, 30, 1, 0, 0, 0, 0, 140, 210, 42, 1, 0, 0, 0, 0, 70, 560, 420, 56, 1, 0, 0, 0, 0, 0, 630, 1680, 756, 72, 1, 0, 0, 0, 0, 0, 252, 3150, 4200, 1260, 90, 1, 0, 0, 0, 0, 0, 0, 2772, 11550, 9240, 1980, 110, 1, 0, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,5


COMMENTS

Row sums are the central trinomial coefficients A002426.
Product of A007318 and this sequence is A008459.
Coefficient array for polynomials P(n,x) = x^n*F(1/2n/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((1x*y)^24*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, nk], {n, 0, 20}, {k, 0, n}]] (* Harvey P. Dale, Nov 12 2014 *)


PROG

(Magma) [[Binomial(n, k)*Binomial(k, nk): k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Jun 14 2015


CROSSREFS

Cf. A063007. A001850 (column sums), A182883.
Sequence in context: A057150 A185663 A262125 * A267163 A357885 A265163
Adjacent sequences: A105865 A105866 A105867 * A105869 A105870 A105871


KEYWORD

easy,nonn,tabl


AUTHOR

Paul Barry, Apr 23 2005


STATUS

approved



