Comtet, Louis; Fiolet, Michel Sur les dérivées successives d’une fonction implicite. (French) Zbl 0307.26011 C. R. Acad. Sci., Paris, Sér. A 278, 249-251 (1974). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 9 Documents MSC: 26B05 Continuity and differentiation questions 05A10 Factorials, binomial coefficients, combinatorial functions PDF BibTeX XML Cite \textit{L. Comtet} and \textit{M. Fiolet}, C. R. Acad. Sci., Paris, Sér. A 278, 249--251 (1974; Zbl 0307.26011) OpenURL Online Encyclopedia of Integer Sequences: Let y=f(x) satisfy F(x,y)=0. The sequence a(n) is the number of terms in the expansion of (d^n/dx^n) y in terms of the partial derivatives of F. E.g.f.: arcsin(x). Expansion of e.g.f.: sin(arctan(x)). E.g.f.: log(1+x)*sinh(x). The n-th derivative of log(1+x)*tanh(x) evaluated at x = 0.