A097194 Row sums of triangle A097190, in which the n-th row polynomial R_n(y) is formed from the initial (n+1) terms of g.f. A097191(y)^(n+1), where R_n(1/3) = 9^n for all n>=0.

1, 25, 649, 17065, 451621, 11998801, 319623445, 8530126057, 227974775239, 6099550226965, 163340461497907, 4377292845062689, 117376545230379631, 3149059523347103293, 84522568856319875179, 2269506752111508954553

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..690

Formula

G.f.: A(x) = 3/((1-27*x) + 2*(1-27*x)^(8/9)).

G.f.: A(x, y) = A097192(x)/(1 - x*A097193(x)).

Maple

seq(coeff(series(3/((1-27*x) +2*(1-27*x)^(8/9)), x, n+1), x, n), n = 0 ..20); # G. C. Greubel, Sep 17 2019

Mathematica

CoefficientList[Series[3/((1-27*x) +2*(1-27*x)^(8/9)), {x, 0, 20}], x] (* G. C. Greubel, Sep 17 2019 *)

Prog

(PARI) a(n)=polcoeff(3/((1-27*x) + 2*(1-27*x+x*O(x^n))^(8/9)), n, x)
(Magma) R<x>:=PowerSeriesRing(Rationals(), 20); Coefficients(R!( 3/((1-27*x) +2*(1-27*x)^(8/9)) )); // G. C. Greubel, Sep 17 2019
(Sage)
def A097194_list(prec):
    P.<x> = PowerSeriesRing(QQ, prec)
    return P(3/((1-27*x) +2*(1-27*x)^(8/9))).list()
A097194_list(20) # G. C. Greubel, Sep 17 2019

Crossrefs

Cf. A097190.

Sequence in context: A152256 A153111 A361712 * A180811 A318183 A015697

Adjacent sequences: A097191 A097192 A097193 * A097195 A097196 A097197

Keyword

nonn

Author

Paul D. Hanna, Aug 03 2004

Status

approved