A290159 Numerators of coefficients in Taylor series expansion of (1+x+x^2)^(1/2).

1, 1, 3, -3, 3, 15, -57, 21, 867, -1893, 1581, 8283, -76953, 34203, 361551, -869691, 6420387, 34130067, -167946159, 79445631, 1696170093, -4239570255, 4083041217, 21859150803, -442212416121, 215805655695, 2316081934929, -5909439428697, 11656013746863, 62663656767603, -322045194694305, 160129270032933, 27589357112530467

Offset: 0

Author

Bruno Zürcher, Jul 22 2017

Keywords

• sign
• frac

Comments

Denominators of the Taylor series expansion are given by A046161.

The terms after the second are divisible by 3.

The sequence of the absolute values is not monotonic.

Crossrefs

Cf. A046161 (denominators).

Programs

Maple

a:= n-> numer(coeff(series(sqrt(1+x+x^2), x, n+3), x, n)):
seq(a(n), n=0..35);  # Alois P. Heinz, Jul 25 2017

Mathematica

Numerator[CoefficientList[Series[Sqrt[1+x+x^2], {x, 0, 32}], x]]

PARI

x = 'x + O('x^40); apply(x->numerator(x), Vec((1+x+x^2)^(1/2))) \\ Michel Marcus, Jul 24 2017