A188622 Row sums of the Riordan matrix (1/sqrt(1-4*x), x/(1-x)) (A187888).

1, 3, 10, 34, 118, 418, 1508, 5524, 20486, 76722, 289580, 1099836, 4198396, 16093236, 61902472, 238805864, 923574598, 3579675026, 13900879132, 54071886764, 210645038548, 821701422716, 3209243934712, 12547819633304, 49109812222108, 192382627198868

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..100 from Vincenzo Librandi)

Formula

D-finite with recurrence: (n+3)*a(n+3) - (7*n+17)*a(n+2) + 2*(7*n+12)*a(n+1) - 4*(2*n+1)*a(n) = 0.

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

Mathematica

CoefficientList[Series[(1-x)/((1-2x)Sqrt[1-4x]), {x, 0, 30}], x] (* Harvey P. Dale, Oct 25 2016 *)

Prog

(Maxima) a(n):=at(diff((1-x)/((1-2*x)*sqrt(1-4*x)), x, n), x=0)/n!;
makelist(a(n), n, 0, 24);
(PARI) x='x+O('x^30); Vec((1-x)/((1-2*x)*sqrt(1-4*x))) \\ G. C. Greubel, Nov 01 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1-x)/((1-2*x)*Sqrt(1-4*x)))); // G. C. Greubel, Nov 01 2018

Crossrefs

Cf. A187888

Sequence in context: A136439 A371819 A178578 * A047017 A026616 A306409

Adjacent sequences: A188619 A188620 A188621 * A188623 A188624 A188625

Keyword

nonn,easy

Author

Emanuele Munarini, Apr 06 2011

Extensions

More terms from Harvey P. Dale, Oct 25 2016

Status

approved