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 A146978 Irregular triangle read by rows: coefficients of the two-variable character of the vertex operator superalgebra A_Ru related to the sporadic simple Rudvalis group. 0
 1, 784, 378, 144452, 92512, 20475, 11327232, 8128792, 2843568, 376740, 40116600, 30421755, 13123110, 3108105, 376740, 20475, 378, 1, 490068257, 373673216, 161446572, 35904960, 3108105, 2096760960, 1649657520, 794670240, 226546320, 35904960, 2843568, 92512, 784 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Note that A_Ru is not the Rudvalis sporadic simple group Ru, rather it is a certain vertex operator superalgebra of rank 28 whose full automorphism group is a direct product of a cyclic group of order seven with Ru. - N. J. A. Sloane, Sep 17 2020 The row index n (the "degree") runs through nonnegative integers and half-integers, while the column index m (the "charge") runs through a finite number of nonnegative even integers (see the table in the Example section). If n is an integer row n has length n+1 (so the maximal index is m=2n); for half-integers n = 1/2, 3/2, 5/2, ... the row lengths are 0, 0, 0, 8, 8, 9, 9, 10, 10... (the pattern of repeated consecutive integers seems to continue). - Andrey Zabolotskiy, Sep 23 2020 Rows of length zero have simply been omitted. LINKS John F. Duncan, Moonshine for Rudvalis's sporadic group I, arXiv:math/0609449 [math.RT], November, 2008 (see pages 51-53) John F. Duncan, Moonshine for Rudvalis's sporadic group II, arXiv:math/0611355 [math.RT], November, 2008 FORMULA T(n+7/2, 2*(7-k)) = T(n+k, 2*k) = T(n+14-k, 28-2*k) for n = 0..3, k = 0..7. Also, T(k, 2*k) = binomial(28, 2*k). - Andrey Zabolotskiy, Feb 18 2019 EXAMPLE Duncan: "The column headed m is the coefficient of p^m (as a series in q) and the row headed n is the coefficient of q^(n-c/24) (as a series in p). The coefficients of p^-m and p^m coincide and all subspaces of odd charge vanish." -------------------------------------------------------------------------| .....|m=0...........|m=2..........|m=4..........|m=6.........|m=8........| -------------------------------------------------------------------------| n=..0|............1.|.............|.............|............|...........| n=1/2|..............|.............|.............|............|...........| n=..1|..........784.|.........378.|.............|............|...........| n=3/2|..............|.............|.............|............|...........| n=..2|.......144452.|.......92512.|.......20475.|............|...........| n=.5/2|.............|.............|.............|............|...........| n=...3|....11327232.|.....8128792.|.....2843568.|.....376740.|...........| n=.7/2|....40116600.|....30421755.|....13123110.|....3108105.|.....376740| n=...4|...490068257.|...373673216.|...161446572.|...35904960.|....3108105| n=.9/2|..2096760960.|..1649657520.|...794670240.|..226546320.|...35904960| n=...5|.13668945136.|.10818453324.|..5284484352.|.1513872360.|..226546320| n=11/2|.56547022140.|.45624923820.|.23757475560.|.7766243940.|.1513872360| -------------------------------------------------------------------------| CROSSREFS Cf. A003918. Sequence in context: A204279 A158399 A007243 * A095954 A351476 A257355 Adjacent sequences: A146975 A146976 A146977 * A146979 A146980 A146981 KEYWORD nonn,tabf AUTHOR Jonathan Vos Post, Nov 04 2008 EXTENSIONS Corrected by Andrey Zabolotskiy, Feb 18 2019 STATUS approved

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Last modified February 8 23:03 EST 2023. Contains 360153 sequences. (Running on oeis4.)