OFFSET
0,5
FORMULA
T(n,n-1) = A245767(n,n-1).
T(n,1) = n*Sum_k Sum_j binomial(n-1,k)*binomial(n-1-k,j) = A027471(n+1).
E.g.f. for column 1 is x*exp(x)^3.
E.g.f. for column 2 is x^2/2*exp(x)^3 + x^2*exp(x)^6 + x^2/2*exp(x)^7.
E.g.f. for column 3 is x^3/3!*exp(x)^15 + x^3/3!*exp(x)^3 + x^3*exp(x)^10 + x^3*exp(x)^12 + x^3/2!*exp(x)^7 + 2*x^3/2!*exp(x)^6 + 2*x^3/2*exp(x)^12.
EXAMPLE
Triangle T(n,k) begins:
1;
1, 1;
1, 6, 4;
1, 27, 66, 29;
1, 108, 780, 1116, 355;
1, 405, 8020, 29250, 28405, 6942;
...
CROSSREFS
KEYWORD
AUTHOR
Geoffrey Critzer, Feb 27 2023
EXTENSIONS
Rows 5 and 6 added by Geoffrey Critzer, Mar 05 2023
STATUS
approved