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A190724 Row sums of Riordan matrix A118384.

%I A190724 #17 Mar 27 2017 03:53:48
%S A190724 1,4,20,106,576,3174,17648,98746,555104,3131854,17720880,100507554,
%T A190724 571179792,3251459670,18535914480,105803208906,604598535360,
%U A190724 3458315246238,19799128470896,113441876080306,650450158678256,3731985710892454,21425304596140080
%N A190724 Row sums of Riordan matrix A118384.
%H A190724 Vincenzo Librandi, <a href="/A190724/b190724.txt">Table of n, a(n) for n = 0..200</a>
%F A190724 a(n) = (6^n+d(n)-sum(6^(k-1)*d(n-k),k=1..n))/2, where d(n) = central Delannoy number (A001850).
%F A190724 G.f.: (1-7*x+sqrt(1-6*x+x^2))/((2-12*x)*sqrt(1-6*x+x^2)).
%F A190724 Recurrence: (n^2+9*n+20)*a(n+5)-8*(3*n^2+23*n+44)*a(n+4)+2*(108*n^2+683*n+1089)*a(n+3)-2*(435*n^2+2159*n+2716)*a(n+2)+(1367*n^2+4917*n+4366)*a(n+1)-210*(n^2+3*n+2)*a(n)=0.
%F A190724 Conjecture: n*(2*n+3)*a(n) +2*(-12*n^2-15*n+22)*a(n-1) +(74*n^2+73*n-274)*a(n-2) -6*(2*n+5)*(n-2)*a(n-3)=0. - _R. J. Mathar_, Jul 24 2012
%F A190724 a(n) ~ (2+sqrt(2))/(2*sqrt(3*sqrt(2)-4)) * (3+2*sqrt(2))^n/sqrt(Pi*n). - _Vaclav Kotesovec_, Oct 20 2012
%t A190724 CoefficientList[Series[(1-7x+Sqrt[1-6x+x^2])/((2-12x)Sqrt[1-6x+x^2]),{x,0,100}],x]
%o A190724 (PARI) x='x+O('x^50); Vec((1-7*x+sqrt(1-6*x+x^2))/((2-12*x)*sqrt(1-6*x+x^2))) \\ _G. C. Greubel_, Mar 26 2017
%Y A190724 Cf. A001850, A118384.
%K A190724 nonn
%O A190724 0,2
%A A190724 _Emanuele Munarini_, May 17 2011