Generating functions for given sequences
Task number: 3868
Construct generating functions for the following sequences. Do not use infinite series in the result:
Variant
\((1{,}1,1{,}1,1{,}1,\ldots)\)
Variant
\((1,-1{,}1,-1{,}1,-1,\ldots)\)
Variant
\((1{,}0,1{,}0,1{,}0,\ldots)\)
Variant
\((1{,}2,3{,}4,5{,}6,\ldots)\)
Variant
\((1,-1{,}2,-2{,}3,-3{,}4,-4,\ldots)\)
Variant
\((2{,}1,4{,}3,6{,}5,\ldots)\)
Variant
\((1{,}2,1{,}4,1{,}8,\ldots)\)
Variant
\((1,-3{,}5,-7{,}9,-11,\ldots)\)
Variant
\((0{,}1,1{,}2,2{,}4,3{,}8,4{,}16,\ldots,i,2^i,\ldots)\)