A190254 Row sums of the Riordan matrix (g(x),x*g(x)), where g(x) = (1-x-sqrt(1-2*x-3*x^2-4*x^3))/(2*x^2*(1+x)) (A190252).

1, 2, 5, 14, 40, 117, 348, 1047, 3179, 9723, 29915, 92498, 287211, 895030, 2797928, 8770635, 27560288, 86792100, 273857035, 865630975, 2740541714, 8689081394, 27586212293, 87688882320, 279055280258, 888981785349, 2834784312290, 9047795153319

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

D-finite with recurrence: 0 = (n^2+17*n+72)*a(n+8) - 4*(2*n^2+31*n+120)*a(n+7) + 2*(7*n^2+101*n+363)*a(n+6) + (19*n^2+203*n+540)*a(n+5) - 3*(9*n^2+81*n+182)*a(n+4) - 2*(28*n^2+269*n+627)*a(n+3) - 36*(n+4)^2*a(n+2) + 3*(11*n^2+31*n+14)*a(n+1) + 6*(2*n^2+7*n+6)*a(n).

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

Mathematica

CoefficientList[Series[(-1+3x+Sqrt[1-2x-3x^2-4x^3])/(2x(1-3x-x^2)), {x, 0, 27}], x]

Prog

(PARI) x='x+O('x^30); Vec((-1+3*x+sqrt(1-2*x-3*x^2-4*x^3))/(2*x*(1-3*x-x^2))) \\ G. C. Greubel, Dec 26 2017

Crossrefs

Cf. A190252.

Sequence in context: A273900 A126220 A136304 * A075496 A114177 A349413

Adjacent sequences: A190251 A190252 A190253 * A190255 A190256 A190257

Keyword

nonn

Author

Emanuele Munarini, May 06 2011

Status

approved