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

0,2

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 )^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

Cf. A118345, A118346, A118348, A118349.

Sequence in context: A229230 A135166 A363574 * A250887 A371577 A334048

Adjacent sequences: A118344 A118345 A118346 * A118348 A118349 A118350

Keyword

nonn

Author

Paul D. Hanna, Apr 26 2006

Status

approved