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Search: id:A115111
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| A115111 |
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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. |
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+0
3
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| 0, 0, 0, 256, 5000, 65880, 739508, 7653632, 75687696, 728589000, 6899424840, 64678048600, 602586261420, 5593531747076, 51815550195500, 479511147907328, 4436081306716064, 41044438822080816, 379913227858140396
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OFFSET
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1,4
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COMMENT
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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.
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FORMULA
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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}.
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EXAMPLE
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a(5)=binomial(20,5)-4*(binomial(15,5)+1)+6*binomial(10,5)=5000.
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CROSSREFS
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Cf. A115246.
Sequence in context: A070056 A074151 A016804 this_sequence A113173 A077072 A128698
Adjacent sequences: A115108 A115109 A115110 this_sequence A115112 A115113 A115114
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KEYWORD
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nonn
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AUTHOR
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Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jan 22 2006
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