Let a generating function: $$(x^n A(x))' $$ How to determine some first term of this sequence. Thanks in advance.
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What do the square brackets denote? – Zubin Mukerjee Jan 26 '15 at 19:42
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1Is $A(x)$ some generating function, e.g. $A(x)=\sum_{k=0}^\infty a_k x^k$? If so just use the product rule and differentiate. – Math1000 Jan 26 '15 at 19:44
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Assuming $A(x) = \sum_{n=0}^\infty a_n n^n$ then
$$ (x^n A(x))' = nx^{n-1} x^n A(x) + x^n A'(x) = nx^{n-1} x^n A(x) + x^n \sum_{n=1}^\infty a_nnx^{n-1}$$
Loreno Heer
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