A197222 Numerators of convergents to e - 1/e.
2, 5, 7, 40, 47, 275, 597, 872, 3213, 36215, 111858, 148073, 704150, 6485423, 7189573, 49622861, 56812434, 220060163, 716992923, 937053086, 4465205267, 9867463620, 14332668887, 24200132507, 86933066408, 111133198915, 420332663153, 1792463851527
Offset: 1
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Mathematica
Numerator[Convergents[E - 1/E, 40]]