SOLUTION: complete the series 3 4 9 34 340 ________ ?

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Question 890249: complete the series
3 4 9 34 340 ________ ?

Found 2 solutions by Edwin McCravy, richwmiller:
Answer by Edwin McCravy(20056) About Me  (Show Source):
Answer by richwmiller(17219) About Me  (Show Source):
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Edwin's answers are correct but his equation is wrong. Most likely a typo.
The first coefficient 5/24 should be 245/24
An=(245/24)*n^4-(1193/12)*n^3+(8239/24)*n^2-(5833/12)*n+235
A1 = 3
A2 = 4
A3 = 9
A4 = 34
A5 = 340
A6 = 1433
A7 = 4064
A8 = 9229
A9 = 18169
A10 = 32370
His equation would yield
An=(5/24)*n^4-(1193/12)*n^3+(8239/24)*n^2-(5833/12)*n+235
A1 = -7
A2 = -156
A3 = -801
A4 = -2526
A5 = -5910
A6 = -11527
A7 = -19946
A8 = -31731
A9 = -47441
A10 = -67630