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A193027
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Decimal expansion of the constant term of the reduction of e^(2x) by x^2->x+1.
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2
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7, 2, 3, 9, 8, 7, 7, 3, 3, 1, 3, 0, 0, 9, 0, 0, 1, 7, 7, 3, 2, 4, 9, 3, 2, 2, 2, 3, 3, 9, 6, 1, 6, 1, 0, 4, 2, 5, 9, 0, 1, 3, 3, 4, 6, 9, 1, 6, 7, 8, 8, 1, 3, 4, 6, 1, 0, 3, 0, 8, 8, 0, 9, 0, 1, 1, 9, 1, 0, 1, 2, 1, 1, 5, 7, 9, 3, 8, 8, 4, 9, 2, 0, 5, 8, 7, 9, 3, 1, 7, 7, 2, 9, 8, 3, 9, 6, 4, 3, 3
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OFFSET
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1,1
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COMMENTS
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Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
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LINKS
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FORMULA
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Equals 1 + Sum_{k>=1} 2^k*Fibonacci(k-1)/k!.
Equals e * (cosh(sqrt(5)) - sinh(sqrt(5))/sqrt(5)). (End)
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EXAMPLE
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7.239877331300900177324932223396161042590133469167...
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MATHEMATICA
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f[x_] := Exp[2 x]; r[n_] := Fibonacci[n];
c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100]
RealDigits[u0, 10]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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