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A118347
Semi-diagonal (one row below central terms) of pendular triangle A118345 and equal to the self-convolution of the central terms (A118346).
4
1, 2, 11, 70, 487, 3592, 27600, 218566, 1771367, 14621410, 122495659, 1038934480, 8903129300, 76970244560, 670507216168, 5879770542870, 51861650744071, 459804626981158, 4095433894576785, 36628711884398086, 328824295880947471
OFFSET
0,2
LINKS
FORMULA
G.f.: ( series_inverse( x*(1-2*x +sqrt((1-2*x)*(1-6*x)))/(2*(1-2*x)) )/x )^2.
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 *)
PROG
(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.<x> = 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
(Magma)
R<x>:=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
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 26 2006
STATUS
approved