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A182186 Number b(n) of basic ideals in the Borel subalgebra of the untwisted affine Lie algebra of type B.

%I A182186 #23 Oct 27 2017 16:34:07
%S A182186 24,128,648,3160,14984,69536,317264,1427912,6355080,28021504,
%T A182186 122586224,532681648,2301267408,9891512000,42327269792,180410129576,
%U A182186 766250022536,3244192404032,13696322822960,57673821115088,242287778611184,1015664308220864,4249246138360928
%N A182186 Number b(n) of basic ideals in the Borel subalgebra of the untwisted affine Lie algebra of type B.
%C A182186 The corresponding sequence for the usual type B Lie algebra is given by the central binomial coefficients A000984.
%H A182186 J. Nilsson, <a href="http://arxiv.org/abs/1204.3771">Enumeration of basic ideals in type B</a>
%H A182186 J. Nilsson, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Nilsson2/nilsson6.html">Enumeration of Basic Ideals in Type B Lie Algebras</a>, J. Int. Seq. 15 (2012) #12.9.5
%F A182186 a(n) = (3*n+5)*2^(2*n-2)-(2*(3*n-1))*binomial(2*n-2, n-1).
%F A182186 a(n) - 8*a(n-1) + 16*a(n-2) = (24/(n-1))*binomial(2*n-6,n-2) for n>3.
%F A182186 -(n-1)*(9*n^2-51*n+76)*a(n) +2*(36*n^3-231*n^2+478*n-295)*a(n-1) -8*(2*n-5)*(9*n^2-33*n+34)*a(n-2)=0. - _R. J. Mathar_, Oct 27 2017
%p A182186 B:=n->(3*n+5)*2^(2*n-2)-(2*(3*n-1))*binomial(2*n-2, n-1): seq(B(n), n=2..30);
%o A182186 (PARI) a(n) = (3*n+5)*2^(2*n-2)-(2*(3*n-1))*binomial(2*n-2, n-1); \\ _Michel Marcus_, Aug 18 2013
%Y A182186 Cf. A000984, A194460.
%K A182186 nonn,easy
%O A182186 2,1
%A A182186 _Jonathan Nilsson_, Apr 16 2012