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%I #7 Mar 17 2021 22:51:11
%S 1,2,11,70,487,3592,27600,218566,1771367,14621410,122495659,
%T 1038934480,8903129300,76970244560,670507216168,5879770542870,
%U 51861650744071,459804626981158,4095433894576785,36628711884398086,328824295880947471
%N Semi-diagonal (one row below central terms) of pendular triangle A118345 and equal to the self-convolution of the central terms (A118346).
%H G. C. Greubel, <a href="/A118347/b118347.txt">Table of n, a(n) for n = 0..500</a>
%F G.f.: ( series_inverse( x*(1-2*x +sqrt((1-2*x)*(1-6*x)))/(2*(1-2*x)) )/x )^2.
%t 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 *)
%o (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)}
%o (Sage)
%o def A118347_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (( x*(1-2*x +sqrt((1-2*x)*(1-6*x)))/(2*(1-2*x)) ).reverse()/x)^2 ).list()
%o A118347_list(31) # _G. C. Greubel_, Mar 17 2021
%o (Magma)
%o R<x>:=PowerSeriesRing(Rationals(), 30);
%o 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
%Y Cf. A118345, A118346, A118348, A118349.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Apr 26 2006
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