|
%I #18 Jan 30 2020 21:29:17
%S 1,0,1,0,1,1,2,3,6,10,19,35,66,125,240,462,897,1750,3431,6756,13357,
%T 26499,52744,105292,210761,422928,850631,1714505,3462538,7005661,
%U 14198718,28823497,58600076,119306476,243224949,496475106,1014616271
%N G.f. 1-(2*x^3)/(-sqrt(-3*x^4-4*x^3-2*x^2+1)-x^2+1).
%F a(n) = sum(k=1..n, (sum(j=0..k, binomial(j,n-k-j)*binomial(k,j)) * binomial(n-k-2,k-1))/k).
%F D-finite with recurrence: (n-1)*n*a(n) = 6*(n-8)*(n-7)*a(n-7) + 2*(5+7*(n-7))*(n-7)*a(n-6) + (24+43*(n-7)+15*(n-7)^2)*a(n-5) + (84+63*(n-7)+11*(n-7)^2)*a(n-4) + (90+40*(n-7)+4*(n-7)^2)*a(n-3) + (30+ 6*(n-7))*a(n-2) - (n-2)*(n-1)*a(n-1). - _Benedict W. J. Irwin_, Sep 25 2016
%F D-finite with recurrence: n*a(n) = -a(n-1) + (2*n - 5)*a(n-2) + (4*n - 17)*a(n-3) + 3*(n-5)*a(n-4). - _Vaclav Kotesovec_, Sep 25 2016
%t Rest[CoefficientList[Series[(1+z(2+z)-Sqrt[-(1+z)(-1+z+z^2+3z^3)])/(2(1+z)), {z, 0, 30}], z]] (* _Benedict W. J. Irwin_, Sep 25 2016 *)
%o (Maxima)
%o a(n):=sum(((sum(binomial(j,n-k-j)*binomial(k,j),j,0,k))*binomial(n-k-2,k-1))/k,k,1,n);
%K nonn
%O 1,7
%A _Vladimir Kruchinin_, Nov 21 2014
|
