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Default How to make Weighted Average

1. I have a column of values in A:A
2. I am trying to make B:B the Weighted Average of A:A where the Weighted
Average is defined as,
WA5 of B3 = (1*A1+2*A2+3*A3+2*A4+1*A5)/(1+2+3+2+1)
WA5 of B4 = (1*A2+2*A3+3*A4+2*A5+1*A6)/(1+2+3+2+1)
WA5 of B5 = (1*A3+2*A4+3*A5+2*A6+1*A7)/(1+2+3+2+1)
You can see B:B will be a smooth version of A:A

Variations can be
WA3 of B3 = (1*A1+2*A2+1*A3)/(1+2+1)
WA3 of B4 = (1*A2+2*A3+1*A4)/(1+2+1)

WA101, WA201 become difficult to be listed as above examples.
Excel array formulas confuses me soon, thank you for your help in advance !

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