組合數(shù)學(xué)答案

1、2.1求序列求序列0，1，8，27，……的母函數(shù)。的母函數(shù)。3n解：??????????????????????nnnxnxxxxGxaxaxaxaaxG3323322102780??046414321313?????????????nnnnnnnaaaaanana左右同乘再連加：0464:0464:0464:0464:4321543211123455012344??????????????????????????????nnnnnnn

2、nnnnnaaaaaxaaaaaxaaaaaxaaaaax??母函數(shù)：????42162036????xxxxG2.2已知序列已知序列……………………，求母函數(shù)。，求母函數(shù)。????3433??33n?解：的第k項(xiàng)為：，對于本題，n=4，1(1)nx??11()knn???母函數(shù)為：?41(1)x?2.3已知母函數(shù)已知母函數(shù)G（X）=求序列求序列25431783xxx???na解：G（X）==)61)(91(783xxx???)61()

3、91(xBxA???從而有：??????????????4778963BABABAG（X）=)61(4)91(7xx????G（X）=7)999x(13322?????xx4))6((6)(6)x(13322??????xx，解得???????????02532531BABA???????????1053510535BA那么，iiiiiiiixxxxBxAxH????????????????????????????????000)253

4、()253(55)253(55)253(55)2531)(253()2531)(253()(2.6求序列求序列1，0，2，0，3，4，0，……，……解：G(x)=10x203004……?2x3x4x3x5x6x=1234……2x4x6xG(x)=23……?2x2x4x6x（1）G（x）=1……?2x2x4x6x（1）G（x）=?2x(22)jjjjjjijvvssvvvvssea?????????????????211x?G（x）=?2

5、21(1)x?2.7設(shè)求。24621234....(1)....nGxxxnx????????222(1)(1)xGxG??題解：2462224682221234....(1)....(1)234....()(1)....(2)nnnGxxxnxxGxxxxnxnx??????????????????（1）（2）得：224621....()....nGxGxxxnx????????2222221(1)1(1)1nnxxGxxGx????