A118348 Semi-diagonal (two rows below central terms) of pendular triangle A118345 and equal to the self-convolution cube of the central terms (A118346).

1, 3, 18, 121, 873, 6606, 51728, 415629, 3407391, 28388847, 239675406, 2045980440, 17629939980, 153142537440, 1339599358944, 11789960853293, 104327344928619, 927627432162129, 8283625668834238, 74259685465582569, 668054892245119353

Offset

0,2

Links

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

Formula

G.f.: ( series_inverse( x*(1-2*x +sqrt((1-2*x)*(1-6*x)))/(2*(1-2*x)) )/x )^3.

Mathematica

CoefficientList[(InverseSeries[Series[x*(1-2*x +Sqrt[(1-2*x)*(1-6*x)])/(2*(1-2*x)), {x, 0, 30}]]/x)^3, 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)^3, 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)^3 ).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)^3 )); // G. C. Greubel, Mar 17 2021

Crossrefs

Cf. A118345, A118346, A118347, A118349.

Sequence in context: A320616 A009065 A109714 * A011792 A295537 A183145

Adjacent sequences: A118345 A118346 A118347 * A118349 A118350 A118351

Keyword

nonn

Author

Paul D. Hanna, Apr 26 2006

Status

approved