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bug in a simple series expansion #38868

@fchapoton

Description

@fchapoton

Steps To Reproduce

sage: var('t')
sage: v = -125/24*e^(-5*t)/t - 8/3*e^(-4*t)/t^2 - 3/2*e^(-3*t)/t^3 - e^(-2*t)/t^4 - e^(-t)/t^5 + 1/t^5; v
-125/24*e^(-5*t)/t - 8/3*e^(-4*t)/t^2 - 3/2*e^(-3*t)/t^3 - e^(-2*t)/t^4 - e^(-t)/t^5 + 1/t^5
sage: v.series(t,2)
54/5 + (-3731/90)*t + Order(t^2)
sage: v.series(t,4)
54/5 + (-29849/720)*t + 139459/1680*t^2 + (-2305729/20160)*t^3 + Order(t^4)
sage: v.series(t,6)
54/5 + (-29849/720)*t + 139459/1680*t^2 + (-1537153/13440)*t^3 + 43947619/362880*t^4 + (-10845131/103680)*t^5 + Order(t^6)

Expected Behavior

answer should be correct up to the required order.

Actual Behavior

last term is always wrong

Additional Information

No response

Environment

  • OS: Ubuntu 24.04
  • Sage Version: 10.5.beta8

Checklist

  • I have searched the existing issues for a bug report that matches the one I want to file, without success.
  • I have read the documentation and troubleshoot guide

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