A193079 Decimal expansion of the constant term of the reduction of sinh(2x) by x^2->x+1.

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

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+1)*Fibonacci(2*k)/(2*k+1)!.

Equals ((3+sqrt(5))*sinh(1-sqrt(5)) + 2*sinh(1+sqrt(5)))/(5 + sqrt(5)). (End)

Example

2.3691586979000944404682728022583852586980...

Mathematica

f[x_] := Sinh[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]

Crossrefs

Cf. A000045, A193010, A192232, A193080.

Sequence in context: A103964 A199790 A088329 * A191397 A358764 A361133

Adjacent sequences: A193076 A193077 A193078 * A193080 A193081 A193082

Keyword

nonn,cons

Author

Clark Kimberling, Jul 15 2011

Status

approved