OFFSET
0,4
FORMULA
G.f. for n-th row: Sum_{k=0..n} binomial(n, k)*((1+x)^k-1)^(n-k). - Vladeta Jovovic, Apr 04 2003
E.g.f.: Sum_{n>=0} exp(y*((1+x)^n-1))*y^n/n!. - Vladeta Jovovic, May 28 2004
T(n,3) = n*(n-1)*(n-2)*(n-3)*(n^2-3*n+4)/6, n>=4. - R. J. Mathar, Mar 16 2021
EXAMPLE
1;
1;
1, 2;
1, 6, 6;
1, 12, 36, 32, 6;
1, 20, 120, 280, 280, 120, 20;
1, 30, 300, 1320, 2910, 3492, 2400, 960, 210, 20;
...
MAPLE
A052296 := proc(n, k)
local x, l ;
add(binomial(n, l)*((1+x)^l-1)^(n-l), l=0..n) ;
expand(%) ;
coeftayl(%, x=0, k) ;
end proc: # R. J. Mathar, Mar 16 2021
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Vladeta Jovovic, Feb 08 2000
STATUS
approved