A193082 Decimal expansion of the coefficient of x in the reduction of cosh(2x) by x^2->x+1.

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

Offset: 1

Author

Clark Kimberling, Jul 15 2011

Keywords

• nonn
• cons

Comments

Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.

Examples

			4.86127014034021114230075809766492371...
		

Crossrefs

Cf. A000045, A193010, A192232, A193081.

Programs

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]

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)