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A190737 Diagonal sums of the Riordan matrix A104259. 2

%I #15 Sep 08 2022 08:45:57

%S 1,2,6,19,66,244,946,3801,15697,66234,284339,1237983,5453611,24263355,

%T 108865901,492051006,2238220336,10238568080,47070014643,217363784060,

%U 1007794226777,4689545704246,21893712581740,102520882301832,481393173378979

%N Diagonal sums of the Riordan matrix A104259.

%H G. C. Greubel, <a href="/A190737/b190737.txt">Table of n, a(n) for n = 0..1000</a>

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

%F 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)

%F + 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).

%F 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

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

%o (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

%o (Magma) m:=30; R<x>:=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

%Y Cf. A104259

%K nonn

%O 0,2

%A _Emanuele Munarini_, May 18 2011

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Last modified July 19 19:50 EDT 2024. Contains 374436 sequences. (Running on oeis4.)