|
| |
|
|
A086456
|
|
Expansion of (1 + x + sqrt(1 - 6*x + x^2))/2 in powers of x.
|
|
4
|
|
|
|
1, -1, -2, -6, -22, -90, -394, -1806, -8558, -41586, -206098, -1037718, -5293446, -27297738, -142078746, -745387038, -3937603038, -20927156706, -111818026018, -600318853926, -3236724317174, -17518619320890, -95149655201962
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Series reversion of x(Sum_{k>=0} a(k)x^k) is x(Sum_{k>=0} A003168(k)x^k).
G.f. A(x) = Sum_{k>=0} a(k)x^k satisfies 0 = 2*x - (x + 1)*A(x) + A(x)^2.
|
|
|
LINKS
|
Table of n, a(n) for n=0..22.
Foissy, Loic, Algebraic structures on double and plane posets, J. Algebr. Comb. 37, No. 1, 39-66 (2013).
|
|
|
FORMULA
|
G.f.: (1 + x + sqrt(1 - 6*x + x^2))/2. (= 1/g.f. A001003)
D-finite with recurrence: n*a(n) + 3*(-2*n + 3)*a(n-1) + (n-3)*a(n-2) = 0. - R. J. Mathar, Jul 23 2017
|
|
|
MATHEMATICA
|
ReciprocalSeries[ser_, n_] := CoefficientList[ Series[1/ser, {x, 0, n}], x];
LittleSchroeder := (1 + x - Sqrt[1 - 6 x + x^2])/(4 x); (* A001003 *)
ReciprocalSeries[LittleSchroeder, 22] (* Peter Luschny, Jan 10 2019 *)
|
|
|
PROG
|
(PARI) a(n)=polcoeff((1+x+sqrt(1-6*x+x^2+x*O(x^n)))/2, n)
|
|
|
CROSSREFS
|
A minor variation of A006318. a(n)=-A006318(n-1), n>0. a(n)=A085403(n), n>1.
Cf. A001003.
Sequence in context: A165523 A049126 A049134 * A155069 A006318 A103137
Adjacent sequences: A086453 A086454 A086455 * A086457 A086458 A086459
|
|
|
KEYWORD
|
sign
|
|
|
AUTHOR
|
Michael Somos, Jul 20 2003
|
|
|
STATUS
|
approved
|
| |
|
|
