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.

1, 12, 204, 3978, 83538, 1837836, 41745132, 970574319, 22970258883, 551286213192, 13381219902024, 327839887599588, 8095123378420596, 201221638263597672, 5030540956589941800, 126392341534322287725

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<x>:=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.<x> = 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