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A053693
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Number of self-conjugate 8-core partitions of n.
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1
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1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 1, 1, 5, 2, 3, 4, 4, 5, 3, 4, 4, 6, 4, 5, 6, 4, 5, 7, 6, 7, 7, 5, 7, 7, 6, 5, 8, 5, 5, 6, 6, 6, 13, 11, 4, 11, 7, 9, 9, 6, 11, 12, 10, 8, 13, 9, 8, 15, 9, 7, 12, 8, 10, 14, 9, 10, 13, 13, 8, 16, 12, 12, 15, 8, 9, 14, 12, 11, 19, 11, 12, 18, 14, 11, 17
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| Euler transform of period 16 sequence [1,-1,1,0,1,-1,1,0,1,-1,1,0,1,-1,1,-4,...].
Expansion of q^(-21/8)eta(q^2)^2eta(q^16)^4/(eta(q)eta(q^4)) in powers of q.
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REFERENCES
| Garvan, F., Kim, D. and Stanton, D., Cranks and t-cores, Inventiones Math. 101 (1990) 1-17
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FORMULA
| G.f.: product((1-q^(16*i))^4*(1-q^(4*i-2))/(1-q^(2*i-1)), i=1..infinity)
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PROG
| (PARI) a(n)=local(X); if(n<0, 0, X=x+x*O(x^n); polcoeff(eta(X^2)^2*eta(X^16)^4/eta(X)/eta(X^4), n))
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CROSSREFS
| Cf. A053692.
Sequence in context: A132011 A054893 A090617 * A068063 A087181 A034973
Adjacent sequences: A053690 A053691 A053692 * A053694 A053695 A053696
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KEYWORD
| easy,nonn
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AUTHOR
| James A. Sellers (sellersj(AT)math.psu.edu), Feb 14 2000
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