11!(n−1)!+13!(n−3)!+15!(n−5)!+....=

We have 1+xn=C0+C1x+C2x2+......+Cnxn(1+x)nn!=C0n!+C1n!x+C2n!x2+--+Cnn!xn If x=1, then 2nn!=1n!+1(n-1)!+12!(n-2)!+--- If x=-1, then 0=1n!-1(n-1)!+22!(n-2)!+… By subtracting, we get 2nn!=21(n-1)!+13!(n-3)!+….∴G.E.=2n-1n!