A109271 Floor of expansion (1+Pi*x)^e.
1, 8, 23, 17, -4, 3, -4, 5, -10, 16, -34, 69, -150, 336, -777, 1833, -4422, 10852, -27053, 68354, -174820, 451966, -1179915, 3107551, -8250149, 22063698, -59402336, 160918012, -438405420, 1200699624, -3304583628, 9136432371, -25367772162, 70715532758, -197863773109, 555569907134
Offset: 1
Keywords
Examples
(1+Pi*x)^e = 1 + e*Pi*x + (1/2)*(e-1)*e*Pi^2*x^2 + ... a(1) = floor(1) = 1. a(2) = floor(e*Pi) = 8. a(3) = floor((1/2)*(e-1)*e*Pi^2) = 23.
Programs
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Mathematica
ns=Normal[With[{m=50}, s=Series[(1+Pi x)^E, {x, 0, m}]]]; A109271=Floor[ CoefficientList[ns, x]]