OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
FORMULA
From Peter Bala, Oct 13 2015: (Start)
n-th row polynomial R(n,t) = [x^n] ( (1 + t*x)*(1 + x)^2 )^n.
Cf. A008459, whose n-th row polynomial is equal to [x^n] ( (1 + t*x)*(1 + x) )^n.
exp( Sum_{n >= 1} R(n,t)*x^n/n ) = 1 + (2 + t)*x + (5 + 6*t + t^2)*x^2 + ... is the o.g.f. for A120986. (End)
EXAMPLE
Triangle begin
n\k| 0 1 2 3 4 5
---------------------------------
0 | 1
1 | 2 1
2 | 6 8 1
3 | 20 45 18 1
4 | 70 224 168 32 1
5 | 252 1050 1200 450 50 1
...
MATHEMATICA
Flatten[Table[Table[Binomial[n, k]Binomial[2n, n-k], {k, 0, n}], {n, 0, 10}]] (* Harvey P. Dale, Aug 10 2011 *)
PROG
(PARI) for(n=0, 10, for(k=0, n, print1(binomial(n, k)*binomial(2*n, n-k), ", "))) \\ G. C. Greubel, Sep 01 2017
(Maxima)
B(x, y):=(sqrt(-x*(4*x^2*y^3+(-12*x^2-8*x)*y^2+(12*x^2-20*x+4)*y-4*x^2+x))/(2*3^(3/2))-(x*(18*y+9)-2)/54)^(1/3);
C(x, y):=-B(x, y)-(x*(3*y-3)+1)/(9*B(x, y))-1/3;
A(x, y):=x*diff(C(x, y), x)*(-1/C(x, y)+1/(1+C(x, y)));
taylor(A(x, y), x, 0, 7, y, 0, 7); /* Vladimir Kruchinin, Sep 24 2018 */
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Jul 30 2005
STATUS
approved