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A146978 The terms of lowest charge and degree in the character of A_Ru, the sporadic simple group of Rudvalis, by rows. 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

LINKS

Table of n, a(n) for n=0..30.

John F. Duncan, Moonshine for Rudvalis's sporadic group I, arXiv:math/0609449 [math.RT], 2008, see p. 53, Table 9.

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

Sequence in context: A204279 A158399 A007243 * A095954 A257355 A187935

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 November 12 22:16 EST 2019. Contains 329079 sequences. (Running on oeis4.)