A097187 Antidiagonal sums of triangle A097186, in which the n-th row polynomial R_n(y) is formed from the initial (n+1) terms of g.f. A057083(y)^(n+1), where R_n(1/3) = 3^n for all n>=0.

1, 1, 7, 10, 58, 94, 499, 868, 4360, 7951, 38407, 72508, 339997, 659380, 3019639, 5984968, 26880052, 54249628, 239683171, 491235070, 2139947788, 4444675456, 19125212575, 40190140696, 171064560433, 363227946394, 1531088393647

Offset: 0

Author

Paul D. Hanna, Aug 03 2004

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A004988, A057083, A097186, A097188.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 3*x/((1-9*x^2) + (3*x-1)*(1-9*x^2)^(2/3)) )); // G. C. Greubel, Sep 17 2019

Maple

seq(coeff(series(3*x/((1-9*x^2) +(3*x-1)*(1-9*x^2)^(2/3)), x, n+2), x, n), n = 0..30); # G. C. Greubel, Sep 17 2019

Mathematica

CoefficientList[Series[3*x/((1-9*x^2) +(3*x-1)*(1-9*x^2)^(2/3)), {x, 0, 30}], x] (* G. C. Greubel, Sep 17 2019 *)

PARI

a(n)=polcoeff(3*x/((1-9*x^2)+(3*x-1)*(1-9*x^2+x^2*O(x^n))^(2/3)), n,x)

Sage

def A097187_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P(3*x/((1-9*x^2) + (3*x-1)*(1-9*x^2)^(2/3))).list()
A097187_list(30) # G. C. Greubel, Sep 17 2019

Formula

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

G.f.: A(x) = A004988(x^2)/(1 - x*A097188(x^2)).