A115111 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.

0, 0, 0, 256, 5000, 65880, 739508, 7653632, 75687696, 728589000, 6899424840, 64678048600, 602586261420, 5593531747076, 51815550195500, 479511147907328, 4436081306716064, 41044438822080816, 379913227858140396

Offset: 1

Author

Hieronymus Fischer, Jan 22 2006

Keywords

• nonn

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.

Examples

			a(5)=binomial(20,5)-4*(binomial(15,5)+1)+6*binomial(10,5)=5000.
		

Crossrefs

Cf. A115246.

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}.