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# [求助] 各位大神求助，不懂算数

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 最简单还是编一个程序算一下

 S(0)=1 S(1)=5 S(2)=15 S(3)=35 S(4)=70 S(5)=126 S(6)=210 S(7)=330 S(8)=495 S(9)=715 S(10)=1001 S(11)=1365 S(12)=1820 S(13)=2380 S(14)=3060 S(15)=3876 S(16)=4845 S(17)=5985 S(18)=7315 S(19)=8855 S(20)=10626 S(21)=12650 S(22)=14950 S(23)=17550 S(24)=20475 S(25)=23751 .......

 这就是带限制条件的不定方程整数解问题。 计算 (1+x+x^2+\cdots+x^{27})^5 并展开，得到$x^{135}+5 x^{134}+15 x^{133}+35 x^{132}+70 x^{131}+126 x^{130}+210 x^{129}+330 x^{128}+495 x^{127}+715 x^{126}+1001 x^{125}+1365 x^{124}+1820 x^{123}+2380 x^{122}+3060 x^{121}+3876 x^{120}+4845 x^{119}+5985 x^{118}+7315 x^{117}+8855 x^{116}+10626 x^{115}+12650 x^{114}+14950 x^{113}+17550 x^{112}+20475 x^{111}+23751 x^{110}+27405 x^{109}+31465 x^{108}+35955 x^{107}+40895 x^{106}+46301 x^{105}+52185 x^{104}+58555 x^{103}+65415 x^{102}+72765 x^{101}+80601 x^{100}+88915 x^{99}+97695 x^{98}+106925 x^{97}+116585 x^{96}+126651 x^{95}+137095 x^{94}+147885 x^{93}+158985 x^{92}+170355 x^{91}+181951 x^{90}+193725 x^{89}+205625 x^{88}+217595 x^{87}+229575 x^{86}+241501 x^{85}+253305 x^{84}+264915 x^{83}+276255 x^{82}+287245 x^{81}+297801 x^{80}+307845 x^{79}+317305 x^{78}+326115 x^{77}+334215 x^{76}+341551 x^{75}+348075 x^{74}+353745 x^{73}+358525 x^{72}+362385 x^{71}+365301 x^{70}+367255 x^{69}+368235 x^{68}+368235 x^{67}+367255 x^{66}+365301 x^{65}+362385 x^{64}+358525 x^{63}+353745 x^{62}+348075 x^{61}+341551 x^{60}+334215 x^{59}+326115 x^{58}+317305 x^{57}+307845 x^{56}+297801 x^{55}+287245 x^{54}+276255 x^{53}+264915 x^{52}+253305 x^{51}+241501 x^{50}+229575 x^{49}+217595 x^{48}+205625 x^{47}+193725 x^{46}+181951 x^{45}+170355 x^{44}+158985 x^{43}+147885 x^{42}+137095 x^{41}+126651 x^{40}+116585 x^{39}+106925 x^{38}+97695 x^{37}+88915 x^{36}+80601 x^{35}+72765 x^{34}+65415 x^{33}+58555 x^{32}+52185 x^{31}+46301 x^{30}+40895 x^{29}+35955 x^{28}+31465 x^{27}+27405 x^{26}+23751 x^{25}+20475 x^{24}+17550 x^{23}+14950 x^{22}+12650 x^{21}+10626 x^{20}+8855 x^{19}+7315 x^{18}+5985 x^{17}+4845 x^{16}+3876 x^{15}+3060 x^{14}+2380 x^{13}+1820 x^{12}+1365 x^{11}+1001 x^{10}+715 x^9+495 x^8+330 x^7+210 x^6+126 x^5+70 x^4+35 x^3+15 x^2+5 x+1$其中每一项的指数代表给定的和，系数就是对应的组合数。 如果给定的和 s 小于27，则组合数可表示为 \D\frac{1}{24} (s+1) (s+2) (s+3) (s+4).

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