The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A097193 G.f. A(x) satisfies A097191(x*A(x)) = A(x) and so equals the ratio of the g.f.s of any two adjacent diagonals of triangle A097190. 5
 1, 12, 204, 3978, 83538, 1837836, 41745132, 970574319, 22970258883, 551286213192, 13381219902024, 327839887599588, 8095123378420596, 201221638263597672, 5030540956589941800, 126392341534322287725 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA G.f.: A(x) = (1-(1-27*x)^(1/9))/(3*x). G.f.: A(x) = (1/x)*(series reversion of x/A097191(x)). a(n) = A097192(n)/(n+1). a(n) ~ 27^n / (Gamma(8/9) * n^(10/9)). - Vaclav Kotesovec, Feb 12 2014 MAPLE seq(coeff(series((1-(1-27*x)^(1/9))/(3*x), x, n+2), x, n), n = 0 ..20); # G. C. Greubel, Sep 17 2019 MATHEMATICA CoefficientList[Series[(1-(1-27*x)^(1/9))/(3*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 12 2014 *) PROG (PARI) a(n)=polcoeff((1-(1-27*x+x^2*O(x^n))^(1/9))/(3*x), n, x) (Magma) R:=PowerSeriesRing(Rationals(), 20); Coefficients(R!( (1-(1-27*x)^(1/9))/(3*x) )); // G. C. Greubel, Sep 17 2019 (Sage) def A097193_list(prec): P. = PowerSeriesRing(QQ, prec) return P((1-(1-27*x)^(1/9))/(3*x)).list() A097193_list(20) # G. C. Greubel, Sep 17 2019 CROSSREFS Cf. A097190, A097191, A097192. Sequence in context: A080316 A357568 A108020 * A051688 A198529 A372616 Adjacent sequences: A097190 A097191 A097192 * A097194 A097195 A097196 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 03 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 17 20:00 EDT 2024. Contains 375990 sequences. (Running on oeis4.)