OFFSET
1,2
FORMULA
Let a(n) = A006472(n), the 'triangular' factorial numbers. Then a(n)/(a(k)*a(n-k)) produces the present triangle (with a different offset). - Peter Bala, Dec 07 2011
T(n,k) = 1/2*(n+1-k)*C(n+1,k)*C(n,k-1), for n,k >= 1. O.g.f.: x*y/((1-x-x*y)^2 - 4*x^2*y)^(3/2) = x*y + x^2*(3*y + 3*y^2) + x^3*(6*y + 18*y^2 + 6*y^3) + .... Cf. A008459 with o.g.f.: x*y/((1-x-x*y)^2 - 4*x^2*y)^(1/2). Sum {k = 1..n-1} T(n,k)*2^(n-k) = A002695(n). - Peter Bala, Apr 10 2012
EXAMPLE
First few rows of the triangle are:
1;
3, 3;
6, 18, 6;
10, 60, 60, 10;
15, 150, 300, 150, 15;
21, 315, 1050, 1050, 315, 21;
...
MAPLE
A132818 := proc(n, k)
(n+1-k)*binomial(n+1, k)*binomial(n, k-1)/2 ;
end proc: # R. J. Mathar, Jul 29 2015
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson, Sep 02 2007
EXTENSIONS
Corrected by R. J. Mathar, Jul 29 2015
STATUS
approved