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A290159
Numerators of coefficients in Taylor series expansion of (1+x+x^2)^(1/2).
0
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.
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
KEYWORD
sign,frac
AUTHOR
Bruno Zürcher, Jul 22 2017
STATUS
approved