A118347 Semi-diagonal (one row below central terms) of pendular triangle A118345 and equal to the self-convolution of the central terms (A118346).

1, 2, 11, 70, 487, 3592, 27600, 218566, 1771367, 14621410, 122495659, 1038934480, 8903129300, 76970244560, 670507216168, 5879770542870, 51861650744071, 459804626981158, 4095433894576785, 36628711884398086, 328824295880947471

Offset: 0

Author

Paul D. Hanna, Apr 26 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A118345, A118346, A118348, A118349.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30);
Coefficients(R!( (Reversion( x*(1-2*x +Sqrt((1-2*x)*(1-6*x)))/(2*(1-2*x)) )/x)^2 )); // G. C. Greubel, Mar 17 2021

Mathematica

CoefficientList[(InverseSeries[Series[x*(1-2*x +Sqrt[(1-2*x)*(1-6*x)])/(2*(1-2*x)), {x, 0, 30}]]/x)^2, x] (* G. C. Greubel, Mar 17 2021 *)

PARI

{a(n) = polcoeff( (serreverse(x*(1-2*x+sqrt((1-2*x)*(1-6*x)+x*O(x^n)))/(2*(1-2*x)))/x)^2,n)}

Sage

def A118347_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (( x*(1-2*x +sqrt((1-2*x)*(1-6*x)))/(2*(1-2*x)) ).reverse()/x)^2 ).list()
A118347_list(31) # G. C. Greubel, Mar 17 2021

Formula

G.f.: ( series_inverse( x*(1-2*x +sqrt((1-2*x)*(1-6*x)))/(2*(1-2*x)) )/x )^2.