A193028 - OEIS

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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

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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