A193028 Decimal expansion of the coefficient of x in the reduction of e^(2x) by x^2->x+1.

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

Offset

2,3

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=2..101.

Formula

From Amiram Eldar, Jan 18 2022: (Start)

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

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

Example

11.244289366951194632995431729275126971...

Mathematica

f[x_] := Exp[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, A193027.

Sequence in context: A122592 A099264 A011172 * A203631 A188424 A220588

Adjacent sequences: A193025 A193026 A193027 * A193029 A193030 A193031

Keyword

nonn,cons

Author

Clark Kimberling, Jul 14 2011

Extensions

Offset corrected by Amiram Eldar, Jan 18 2022

Status

approved