A097185 Row sums of triangle A097181, in which the n-th row polynomial R_n(y) is formed from the initial (n+1) terms of g.f. A097182(y)^(n+1), where R_n(1/2) = 8^n for all n>=0.

1, 15, 232, 3627, 57016, 899298, 14216560, 225110307, 3568890328, 56635884470, 899474459280, 14294357356110, 227286593929136, 3615608476770340, 57538659207907552, 915981394162628387, 14586262906867731096

Offset: 0

Author

Paul D. Hanna, Aug 03 2004

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..825

Crossrefs

Cf. A097181, A097182.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/((1-16*x) + (1-16*x)^(7/8)) )); // G. C. Greubel, Sep 17 2019

Maple

seq(coeff(series(2/((1-16*x) + (1-16*x)^(7/8)), x, n+1), x, n), n = 0 ..30); # G. C. Greubel, Sep 17 2019

Mathematica

CoefficientList[Series[2/((1-16*x) +(1-16*x)^(7/8)), {x,0,30}], x] (* G. C. Greubel, Sep 17 2019 *)

PARI

a(n)=polcoeff(2/((1-16*x)+(1-16*x+x*O(x^n))^(7/8)),n,x)

Sage

def A097185_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P(2/((1-16*x) + (1-16*x)^(7/8))).list()
A097185_list(30) # G. C. Greubel, Sep 17 2019

Formula

G.f.: A(x) = 2/((1-16*x) + (1-16*x)^(7/8)).