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

1,4

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.

Links

Table of n, a(n) for n=1..19.

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

Cf. A115246.

Sequence in context: A200843 A074151 A016804 * A200790 A206110 A196152

Adjacent sequences: A115108 A115109 A115110 * A115112 A115113 A115114

Keyword

nonn

Author

Hieronymus Fischer, Jan 22 2006

Status

approved