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

0,3

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.

Links

Table of n, a(n) for n=0..32.

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]]

Prog

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

Crossrefs

Cf. A046161 (denominators).

Sequence in context: A110668 A367773 A176248 * A356388 A083562 A332860

Adjacent sequences: A290156 A290157 A290158 * A290160 A290161 A290162

Keyword

sign,frac

Author

Bruno Zürcher, Jul 22 2017

Status

approved