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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

%I

%S 0,0,0,256,5000,65880,739508,7653632,75687696,728589000,6899424840,

%T 64678048600,602586261420,5593531747076,51815550195500,

%U 479511147907328,4436081306716064,41044438822080816,379913227858140396

%N 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.

%C 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.

%F 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}.

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

%Y Cf. A115246.

%K nonn

%O 1,4

%A _Hieronymus Fischer_, Jan 22 2006

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Last modified October 17 02:04 EDT 2019. Contains 328106 sequences. (Running on oeis4.)