Journal of Integer Sequences, Vol. 24 (2021), Article 21.8.6

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


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,    dvi,    ps,    latex    

(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.

Return to Journal of Integer Sequences home page