A190737 Diagonal sums of the Riordan matrix A104259.

1, 2, 6, 19, 66, 244, 946, 3801, 15697, 66234, 284339, 1237983, 5453611, 24263355, 108865901, 492051006, 2238220336, 10238568080, 47070014643, 217363784060, 1007794226777, 4689545704246, 21893712581740, 102520882301832, 481393173378979

Offset: 0

Author

Emanuele Munarini, May 18 2011

Keywords

• nonn

Links

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

Crossrefs

Cf. A104259

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1-x-2*x^2-Sqrt(1-6*x+5*x^2))/(2*x*(1-2*x+x^2+x^3)))); // G. C. Greubel, Apr 23 2018

Mathematica

CoefficientList[Series[(1-x-2x^2-Sqrt[1-6x+5x^2])/(2x(1-2x+x^2+x^3)),{x,0,24}],x]

PARI

x='x+O('x^30); Vec((1-x-2*x^2-sqrt(1-6*x+5*x^2))/(2*x*(1-2*x +x^2 +x^3))) \\ G. C. Greubel, Apr 23 2018

Formula

G.f.: (1-x-2*x^2-sqrt(1-6*x+5*x^2))/(2*x*(1-2*x+x^2+x^3)).

Recurrence: 0 = (n^2+17*n+72)*a(n+8) - (11*n^2+169*n+648)*a(n+7) + 3*(17*n^2+227*n+758)*a(n+6) - 2*(73*n^2+812*n+2259)*a(n+5)

+ 6*(41*n^2+375*n+846)*a(n+4) - (217*n^2+1559*n+2634)*a(n+3) + 3*(17*n^2+29*n-136)*a(n+2) + 10*(5*n^2+43*n+84)*a(n+1) - 25*(n^2+5*n+6)*a(n).

D-finite with recurrence: (n+1)*a(n) +(-8*n+1)*a(n-1) +3*(6*n-5)*a(n-2) +3*(-5*n+8)*a(n-3) +(-n-7)*a(n-4) +5*(n-2)*a(n-5)=0. - R. J. Mathar, Feb 24 2020