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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 21 00:49 EDT 2019. Contains 325189 sequences. (Running on oeis4.)