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A182186
Number b(n) of basic ideals in the Borel subalgebra of the untwisted affine Lie algebra of type B.
0
24, 128, 648, 3160, 14984, 69536, 317264, 1427912, 6355080, 28021504, 122586224, 532681648, 2301267408, 9891512000, 42327269792, 180410129576, 766250022536, 3244192404032, 13696322822960, 57673821115088, 242287778611184, 1015664308220864, 4249246138360928
OFFSET
2,1
COMMENTS
The corresponding sequence for the usual type B Lie algebra is given by the central binomial coefficients A000984.
FORMULA
a(n) = (3*n+5)*2^(2*n-2)-(2*(3*n-1))*binomial(2*n-2, n-1).
a(n) - 8*a(n-1) + 16*a(n-2) = (24/(n-1))*binomial(2*n-6,n-2) for n>3.
-(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
MAPLE
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);
PROG
(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
CROSSREFS
Sequence in context: A044737 A305159 A326367 * A188304 A167981 A185490
KEYWORD
nonn,easy
AUTHOR
Jonathan Nilsson, Apr 16 2012
STATUS
approved