A279633 - OEIS

A279633

Coefficients in the expansion of ([s] + [2s]x + [3s]x^2 + ...)/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = e/2, s = r/(1-r).

3, 1, -3, 2, 3, -7, 1, 14, -16, -13, 45, -19, -70, 104, 38, -242, 162, 321, -636, -14, 1273, -1214, -1335, 3704, -970, -6387, 8154, 4682, -20708, 10944, 30309, -51241, -9990, 111177, -88723, -133479, 305883, -34310, -571978, 626110, 521149, -1747919, 674248

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OFFSET

0,1

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: ([s] + [2s]x + [3s]x^2 + ...)/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = e/2, s = r/(1-r).

MATHEMATICA

z = 100;

r = E/2; f[x_] := f[x] = Sum[Floor[r*(k + 1)] x^k, {k, 0, z}];

s = r/(r - 1); g[x_] := g[x] = Sum[Floor[s*(k + 1)] x^k, {k, 0, z}]

CoefficientList[Series[g[x]/f[x], {x, 0, z}], x]