A193016 Decimal expansion of the coefficient of x in the reduction of sinh(x) by x^2->x+1.

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

Offset

1,2

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

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

Example

1.3776753274909465462115651210703917736958351560...

Mathematica

f[x_] := Sinh[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, A193015.

Sequence in context: A246848 A019634 A123879 * A349604 A325894 A370517

Adjacent sequences: A193013 A193014 A193015 * A193017 A193018 A193019

Keyword

nonn,cons

Author

Clark Kimberling, Jul 14 2011

Status

approved