OFFSET
0,6
LINKS
K. N. Boyadzhiev, Series with central binomial coefficients, Catalan numbers, and harmonic numbers, J. Integer Seq. 15 (2012), Article 12.1.7.
FORMULA
T(n,k) = A211402(n,k)/(2^(n-k)).
T(n,k) = k*T(n-1,k) + (2*k-1)*T(n-1,k-1), T(0,0) = 1, T(n,k) = 0 if k<0 or if k>n.
G.f.: F(x,t) = 1 + x*t + (x+3*x^2)*t^2/2! + (x+9*x^2+15*x^3)*t^3/3! + ... = Sum_{n = 0..inf} R(n,x)* t^n/n!.
The row polynomials R(n,x) satisfy the recursion R(n+1,x) = (x+2*x^2)*R'(n,x) + x*R(n,x) where ' indicates differentiation with respect to x.
R(n,x) = 1/sqrt(1 + 2*x)*Sum_{k >= 0} binomial(2*k,k)/2^k*k^n * x^k/(1 + 2*x)^k (see Boyadzhiev, eqn. 19). - Peter Bala, Jan 18 2018
EXAMPLE
Triangle begins :
1
0, 1
0, 1, 3
0, 1, 9, 15
0, 1, 21, 90, 105
0, 1, 45, 375, 1050, 945
0, 1, 93, 1350, 6825, 14175, 10395
CROSSREFS
KEYWORD
AUTHOR
Philippe Deléham, Feb 10 2013
STATUS
approved