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

Author

Emanuele Munarini, Apr 06 2011

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A187888

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1-x)/((1-2*x)*Sqrt(1-4*x)))); // G. C. Greubel, Nov 01 2018

Mathematica

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

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

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)).

Extensions

More terms from Harvey P. Dale, Oct 25 2016