what is the value of coefficient of x^9 in expansion (1+x)(1+x^2 ) (1+x^3 )(1+x^4 )×...×(1+x^(100) ) ?


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Question Number 93450 by john santu last updated on 13/May/20

$what is the value of coefficient$ $of x^{9} in expansion (1 + x) (1 + x^{2})$ $(1 + x^{3}) (1 + x^{4}) \times . . . \times (1 + x^{100}) ?$
	Answered by john santu last updated on 13/May/20

	Answered by mr W last updated on 13/May/20

	$i t i s t h e n u m b e r o f p a r t i t i o n s f r o m 9$ $i n t o d i s t i n c t p a r t s, w h i c h i s q (9) = 8 .$ $s i m i l a r l y$ $t h e c o e f . o f x^{5} = q (5) = 3 .$ $t h e c o e f . o f x^{12} = q (12) = 15 .$ $t h e c o e f . o f x^{50} = q (50) = 3658 .$
	Commented by john santu last updated on 13/May/20

	$what formula to get it ?$
	Commented by mr W last updated on 14/May/20

	$t h e r e i s n o c l o s e d f o r m u l a f o r q (n) .$ $s e e f o l l o w i n g :$
	Commented by mr W last updated on 14/May/20

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