Original entry on oeis.org
1, 1488, 947304, 335950912, 72474624276, 9790124955552, 833107628914688, 45630592148400000, 1754954450906393538, 51062104386000089648, 1186840963302480101376, 22924552119951492244800, 378933532779364657975000
Offset: 0
(q*j(q))^(k/24):
A289397 (k=-1),
A106205 (k=1),
A289297 (k=2),
A289298 (k=3),
A289299 (k=4),
A289300 (k=5),
A289301 (k=6),
A289302 (k=7),
A007245 (k=8),
A289303 (k=9),
A289304 (k=10),
A289305 (k=11),
A161361 (k=12),
A028512 (k=16),
A028513 (k=32),
A028514 (k=40), this sequence (k=48),
A288846 (k=72).
-
CoefficientList[Series[(QPochhammer[x, x^2]^8 + 256*x/QPochhammer[x, x^2]^16)^6, {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 29 2017 *)
A288846
Expansion of (q*j)^3, where j is a modular function A000521.
Original entry on oeis.org
1, 2232, 2251260, 1355202240, 541778118390, 151522053809760, 30456116651640888, 4460775211418664960, 479919718908048515625, 38292247221915373896560, 2309356967925215526546564, 108570959012192293978767360, 4111854826236389868361040550
Offset: 0
(q*j(q))^(k/24):
A289397 (k=-1),
A106205 (k=1),
A289297 (k=2),
A289298 (k=3),
A289299 (k=4),
A289300 (k=5),
A289301 (k=6),
A289302 (k=7),
A007245 (k=8),
A289303 (k=9),
A289304 (k=10),
A289305 (k=11),
A161361 (k=12),
A028512 (k=16),
A028513 (k=32),
A028514 (k=40),
A028515 (k=48), this sequence (k=72).
-
CoefficientList[Series[(QPochhammer[x, x^2]^8 + 256*x/QPochhammer[x, x^2]^16)^9, {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 29 2017 *)
(q*1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^3 + O[q]^13 // CoefficientList[#, q]& (* Jean-François Alcover, Nov 02 2017 *)
A028512
Character of extremal vertex operator algebra of rank 16.
Original entry on oeis.org
1, 496, 69752, 2115008, 34670620, 394460000, 3499148224, 25817318016, 165011628166, 939112182480, 4853601292512, 23116070653888, 102602164703800, 428200065370144, 1692346392263680, 6371305129660032
Offset: 0
- G. Hoehn, Selbstduale Vertexoperatorsuperalgebren und das Babymonster, Bonner Mathematische Schriften, Vol. 286 (1996), 1-85.
- Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Seiichi Manyama)
- G. Hoehn (gerald(AT)math.ksu.edu), Selbstduale Vertexoperatorsuperalgebren und das Babymonster, Doctoral Dissertation, Univ. Bonn, Jul 15 1995 (pdf, ps).
(q*j(q))^(k/24):
A289397 (k=-1),
A106205 (k=1),
A289297 (k=2),
A289298 (k=3),
A289299 (k=4),
A289300 (k=5),
A289301 (k=6),
A289302 (k=7),
A007245 (k=8),
A289303 (k=9),
A289304 (k=10),
A289305 (k=11),
A161361 (k=12), this sequence (k=16),
A028513 (k=32),
A028514 (k=40),
A028515 (k=48).
-
CoefficientList[Series[(QPochhammer[x, x^2]^8 + 256*x/QPochhammer[x, x^2]^16)^2, {x, 0, 20}], x] (* Vaclav Kotesovec, Jul 15 2017 *)
CoefficientList[Series[(65536 + x*QPochhammer[-1, x]^24)^2 / (2*QPochhammer[-1, x])^16, {x, 0, 20}], x] (* Vaclav Kotesovec, Sep 23 2017 *)
Original entry on oeis.org
1, 992, 385520, 73424000, 7032770680, 330234251072, 9708251628992, 205208814844160, 3384709979113500, 45920987396301280, 531402725344000864, 5384625599438260096, 48726640432968418240, 399835655086212744000
Offset: 0
(q*j(q))^(k/24):
A289397 (k=-1),
A106205 (k=1),
A289297 (k=2),
A289298 (k=3),
A289299 (k=4),
A289300 (k=5),
A289301 (k=6),
A289302 (k=7),
A007245 (k=8),
A289303 (k=9),
A289304 (k=10),
A289305 (k=11),
A161361 (k=12),
A028512 (k=16), this sequence (k=32),
A028514 (k=40),
A028515 (k=48).
-
CoefficientList[Series[(QPochhammer[x, x^2]^8 + 256*x/QPochhammer[x, x^2]^16)^4, {x, 0, 20}], x] (* Vaclav Kotesovec, Jul 15 2017 *)
Showing 1-4 of 4 results.