A097183 Main diagonal 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, 14, 210, 3220, 49910, 778596, 12198004, 191682920, 3019005990, 47633205620, 752604648796, 11904837171864, 188493255221180, 2986893121197160, 47363590921840680, 751502309293205456, 11930099160029636614

Offset: 0

Author

Paul D. Hanna, Aug 03 2004

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A097181, A097182, A097184.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 20); Coefficients(R!( (1-16*x)^(-7/8) )); // G. C. Greubel, Sep 17 2019

Maple

seq(coeff(series((1-16*x)^(-7/8), x, n+1), x, n), n = 0 ..20); # G. C. Greubel, Sep 17 2019

Mathematica

Table[FullSimplify[(n+1)*16^n*Gamma[n+7/8]/(Gamma[7/8]*Gamma[n+2])], {n, 0, 20}] (* Vaclav Kotesovec, Feb 09 2014 *)
CoefficientList[Series[(1-16*x)^(-7/8), {x,0,20}], x] (* G. C. Greubel, Sep 17 2019 *)

PARI

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

Sage

def A097183_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P((1-16*x)^(-7/8)).list()
A097183_list(20) # G. C. Greubel, Sep 17 2019

Formula

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

a(n) = (n+1)*A097184(n).

a(n) = (n+1) * 16^n * Gamma(n+7/8) / (Gamma(7/8) * Gamma(n+2)). - Vaclav Kotesovec, Feb 09 2014