OFFSET
1,4
COMMENTS
The number of different ways to select n elements from four sets of n elements under the precondition of choosing at least one element from each set.
FORMULA
a(n) = binomial(4*n, n)-4*(binomial(3*n, n)+1)+6*binomial(2*n, n); also: a(n)=sum{binomial(n, i)*binomial(n, j)*binomial(n, k)*binomial(n, l)|i, j, k, l=1...(n-3), i+j+k+l=n}.
EXAMPLE
a(5)=binomial(20,5)-4*(binomial(15,5)+1)+6*binomial(10,5)=5000.
CROSSREFS
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Jan 22 2006
STATUS
approved