Solution of the Differential Equation
y(k) = eay,
Special Values of Bell Polynomials, and (k, a)-Autonomous Coefficients
Ronald Orozco López
Departamento de Matemáticas
Universidad de los Andes
Bogotá 111711
Colombia
Abstract:
We give special values of Bell polynomials by using the power series
solution of the equation
y(k) = eay.
In addition, we define
complete and partial exponential autonomous functions, exponential
autonomous polynomials, autonomous polynomials,
and (k, a)-autonomous
coefficients. Finally, we demonstrate the relationship between various numbers
counting combinatorial objects and binomial coefficients, Stirling
numbers of the second kind, and autonomous coefficients.
Full version: pdf,
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(Concerned with sequences
A000111
A000295
A000367
A002105
A002445
A007548
A018893
A027778
A050534
A336020.)
Received April 3 2021; revised versions received April 8 2021; July 26 2021; August 1 2021; August 6 2021.
Published in Journal of Integer Sequences,
August 17 2021.
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