A193080 Decimal expansion of the coefficient of x in the reduction of sinh(2x) by x^2->x+1.

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

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>=0} 2^(2*k+1)*Fibonacci(2*k+1)/(2*k+1)!.

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

Example

6.3830192266109834906946736316102032592390...

Mathematica

f[x_] := Sinh[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, A193079.

Sequence in context: A021098 A307110 A307731 * A197135 A365522 A088246

Adjacent sequences: A193077 A193078 A193079 * A193081 A193082 A193083

Keyword

nonn,cons

Author

Clark Kimberling, Jul 15 2011

Status

approved