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 A193082 Decimal expansion of the coefficient of x in the reduction of cosh(2x) by x^2->x+1. 2
 4, 8, 6, 1, 2, 7, 0, 1, 4, 0, 3, 4, 0, 2, 1, 1, 1, 4, 2, 3, 0, 0, 7, 5, 8, 0, 9, 7, 6, 6, 4, 9, 2, 3, 7, 1, 2, 1, 7, 5, 4, 3, 9, 0, 0, 6, 8, 9, 0, 7, 1, 9, 8, 6, 0, 7, 7, 7, 3, 2, 1, 0, 7, 2, 6, 6, 0, 4, 0, 0, 8, 4, 1, 0, 3, 2, 7, 5, 0, 7, 6, 8, 4, 6, 2, 7, 2, 8, 9, 6, 0, 3, 3, 8, 7, 7, 4, 4, 0, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010. LINKS Table of n, a(n) for n=1..100. FORMULA From Amiram Eldar, Jan 18 2022: (Start) Equals Sum_{k>=1} 2^(2*k)*Fibonacci(2*k)/(2*k)!. Equals 2*sinh(1)*sinh(sqrt(5))/sqrt(5). (End) EXAMPLE 4.86127014034021114230075809766492371... MATHEMATICA f[x_] := Cosh[2 x]; r[n_] := Fibonacci[n]; c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n] u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100] RealDigits[u1, 10] CROSSREFS Cf. A000045, A193010, A192232, A193081. Sequence in context: A005133 A198241 A175475 * A348563 A201335 A338942 Adjacent sequences: A193079 A193080 A193081 * A193083 A193084 A193085 KEYWORD nonn,cons AUTHOR Clark Kimberling, Jul 15 2011 STATUS approved

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Last modified May 21 07:02 EDT 2024. Contains 372729 sequences. (Running on oeis4.)