Binomial Summations 6

Algebra Level 5

If the expansion of (1+x+2x2)20(1+x+2x^2)^{20} is equal to a0+a1x+a2x2++a40x40a_0 + a_1 x+ a_2 x^2 + \cdots + a_{40} x^{40} for constants a0,a1,,a40a_0,a_1, \ldots , a_{40} , compute

1108r=019a2r. \left \lceil \dfrac1{10^8} \sum_{r=0}^{19} a_{2r} \right \rceil .

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