A193029 - OEIS

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A193029

Decimal expansion of the constant term of the reduction of e^(x/2) by x^2->x+1.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,3

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=1..100.

FORMULA

From Amiram Eldar, Jan 18 2022: (Start)

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

Equals exp(1/4)*(cosh(sqrt(5)/4) - sqrt(5)*sinh(sqrt(5)/4)/5). (End)

EXAMPLE