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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.
2
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.
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
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Jan 22 2006
STATUS
approved