OFFSET
3,2
COMMENTS
The row length sequence for this array is A004396(n-2)=floor((2*n-3)/3), n>=3: [1,1,2,3,3,4,5,5,6,7,7,8,9,9,10,...].
The g.f. G(m,x) for the m-th column sequence (with leading zeros) of array A078741 is given there. The recurrence is G(m,x) = x*(3*fallfac(m-1,2)*G(m-1,x) + 3*(m-2)*G(m-2,x) + G(m-3,x))/(1-fallfac(m,3)*x), m>=4, with inputs G(1,x)=0=G(2,x) and G(3,x)=x/(1-(3*2*1)*x); where fallfac(n,m) := A008279(n,m) (falling factorials). Computed from the Blasiak et al. reference, eqs. (20) and (21) with r=3: recurrence for S_{3,3}(n,k).
LINKS
W. Lang, First 11 rows.
FORMULA
EXAMPLE
[1]; [18]; [9,423]; [1,672,14400]; [243,47520,648000]; ...
G(4,x)/(x^2) = 18/((1-3*2*1*x)*(1-4*3*2*x)). kmax(4)=0, hence P(4,x)=a(4,0)=18; x^2 from x^ceiling(4/3).
CROSSREFS
KEYWORD
nonn,easy,tabf
AUTHOR
Wolfdieter Lang, Dec 01 2003
STATUS
approved