cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A109271 Floor of expansion (1+Pi*x)^e.

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%I A109271 #7 Sep 03 2024 08:25:57
%S A109271 1,8,23,17,-4,3,-4,5,-10,16,-34,69,-150,336,-777,1833,-4422,10852,
%T A109271 -27053,68354,-174820,451966,-1179915,3107551,-8250149,22063698,
%U A109271 -59402336,160918012,-438405420,1200699624,-3304583628,9136432371,-25367772162,70715532758,-197863773109,555569907134
%N A109271 Floor of expansion (1+Pi*x)^e.
%e A109271 (1+Pi*x)^e = 1 + e*Pi*x + (1/2)*(e-1)*e*Pi^2*x^2 + ...
%e A109271 a(1) = floor(1) = 1.
%e A109271 a(2) = floor(e*Pi) = 8.
%e A109271 a(3) = floor((1/2)*(e-1)*e*Pi^2) = 23.
%t A109271 ns=Normal[With[{m=50}, s=Series[(1+Pi x)^E, {x, 0, m}]]]; A109271=Floor[ CoefficientList[ns, x]]
%Y A109271 Cf. A075190, A109272.
%K A109271 sign
%O A109271 1,2
%A A109271 _Zak Seidov_, Jun 24 2005