A193025 Decimal expansion of the coefficient of x in the reduction of cosh(x) by x^2->x+1.

6, 3, 6, 6, 4, 7, 4, 0, 5, 9, 6, 7, 3, 6, 9, 1, 9, 0, 3, 6, 9, 7, 8, 1, 1, 3, 4, 3, 9, 9, 3, 6, 7, 3, 6, 1, 9, 6, 3, 2, 7, 6, 3, 1, 3, 5, 3, 9, 8, 1, 1, 9, 8, 1, 8, 4, 1, 5, 1, 8, 7, 8, 4, 0, 9, 8, 1, 8, 7, 0, 4, 7, 6, 1, 0, 3, 0, 9, 5, 3, 3, 4, 9, 2, 9, 9, 2, 2, 5, 4, 8, 9, 2, 3, 7, 1, 0, 9, 5, 0

Offset

0,1

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=0..99.

Formula

From Amiram Eldar, Jan 18 2022: (Start)

Equals Sum_{k>=1} Fibonacci(2*k)/(2*k)!.

Equals (e-1)*sinh(sqrt(5)/2)/sqrt(5*e). (End)

Example

0.6366474059673691903697811343993673619632...

Mathematica

f[x_] := Cosh[x]; r[n_] := Fibonacci[n];
c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
u1 = N[Sum[c[n]*r[n], {n, 0, 300}], 100]
RealDigits[u1, 10]

Crossrefs

Cf. A000045, A193010, A192232, A193017.

Sequence in context: A137245 A060294 A181171 * A021615 A198937 A198867

Adjacent sequences: A193022 A193023 A193024 * A193026 A193027 A193028

Keyword

nonn,cons

Author

Clark Kimberling, Jul 14 2011

Status

approved