A162548 A Chebyshev transform of the little Schroeder numbers A001003.

1, 1, 2, 9, 37, 156, 695, 3203, 15118, 72739, 355475, 1759624, 8804341, 44457125, 226256114, 1159387253, 5976713665, 30974296468, 161285018771, 843388543471, 4427120165182, 23319497761799, 123221525405447, 652989260163472

Offset

0,3

Comments

Hankel transform is Somos-4 variant A162546.

Links

Fung Lam, Table of n, a(n) for n = 0..1335

Formula

G.f.: (1/(1+x^2))*s(x/(1+x^2)), s(x) the g.f. of A001003.

G.f.: (1+x+x^2 - sqrt(1-6*x+3*x^2-6*x^3+x^4))/(4*x*(1+x^2)).

G.f.: 1/(1+x^2-x/(1-2*x/(1+x^2-x/(1-2*x/(1+x^2-x/(1-2*x/(1+x+x^2/(1-... (continued fraction);

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*C(n-k,k)*A001003(n-2k).

Conjecture: (n+1)*a(n) +3*(-2*n+1)*a(n-1) +(4*n-5)*a(n-2) +12*(-n+2)*a(n-3) +(4*n-11)*a(n-4) +3*(-2*n+7)*a(n-5) +(n-5)*a(n-6)=0. - R. J. Mathar, Nov 15 2012. (Formula verified and used for computations. - Fung Lam, Feb 19 2014)

Mathematica

CoefficientList[Series[(1+x+x^2 -Sqrt[1-6*x+3*x^2-6*x^3+x^4])/(4*x*(1+x^2)), {x, 0, 30}], x] (* G. C. Greubel, Feb 26 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec((1+x+x^2 -sqrt(1-6*x+3*x^2-6*x^3+x^4))/( 4*x*(1+x^2))) \\ G. C. Greubel, Feb 26 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (1+x+x^2 -Sqrt(1-6*x+3*x^2-6*x^3+x^4))/(4*x*(1+x^2)) )); // G. C. Greubel, Feb 26 2019
(Sage) ((1+x+x^2 -sqrt(1-6*x+3*x^2-6*x^3+x^4))/(4*x*(1+x^2))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Feb 26 2019

Crossrefs

Cf. A001003, A162543.

Sequence in context: A012493 A106851 A129169 * A150983 A150984 A150985

Adjacent sequences: A162545 A162546 A162547 * A162549 A162550 A162551

Keyword

easy,nonn

Author

Paul Barry, Jul 05 2009

Status

approved