cp's OEIS Frontend

A115791 Number of different ways to select n elements from five sets of n elements under the precondition of choosing at least one element from each set.

%I A115791 #5 Nov 21 2013 12:48:47
%S A115791 0,0,0,0,3125,97200,1932805,31539200,461828790,6332578125,83235183075,
%T A115791 1063505908080,13327125965725,164758298214965,2017489363833125,
%U A115791 24538128923443200,297028957324770140,3583456866615114630
%N A115791 Number of different ways to select n elements from five sets of n elements under the precondition of choosing at least one element from each set.
%C A115791 The number of different ways to select n elements from five sets of n elements under the precondition of choosing at least one element from each set.
%F A115791 a(n) = binomial(5*n,n)-5*binomial(4*n,n)+10*binomial(3*n,n)-10*binomial(2*n,n)+5; ; also: a(n)=sum{binomial(n,i)*binomial(n,j)*binomial(n,k)*binomial(n,l)*binomial(n,m)||i,j,k,l,m=1...(n-4),i+j+k+l+m=n}. General formula for N sets with m elements each: the number of different ways to select k elements from j different sets: G(N,m,j,k) = binomial(N,j)*sum(binomial(j,i)*binomial(i*m,k)*(-1)^i*(-1)^j|i=1...j); Recursion formula: G(N,m,j,k) = binomial(N,j)*binomial(j*m,k) - sum(binomial(N-i,j-i)*G(N,m,i,k)|i=1...j-1);
%e A115791 a(6)=binomial(30,6)-5*binomial(24,6)+10*binomial(18,6)-10*binomial(12,6)+5=97200;
%t A115791 Table[Binomial[5n,n]-5Binomial[4n,n]+10Binomial[3n,n]-10Binomial[2n,n]+5,{n,20}] (* _Harvey P. Dale_, Nov 06 2011 *)
%Y A115791 Cf. A115111, A115112, A115246.
%K A115791 nonn
%O A115791 1,5
%A A115791 _Hieronymus Fischer_, Jan 31 2006