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Search: id:A081622
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| A081622 |
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Number of 6-core partitions of n. |
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+0
2
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| 1, 1, 2, 3, 5, 7, 5, 9, 10, 12, 12, 14, 20, 20, 21, 23, 24, 24, 32, 29, 35, 36, 44, 47, 38, 47, 49, 52, 55, 58, 59, 64, 66, 71, 70, 78, 79, 88, 87, 90, 85, 87, 111, 104, 102, 107, 112, 113, 121, 113, 130, 130, 148, 153, 132, 147, 149, 156, 162, 149, 167, 160, 178, 180
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Euler transform of period 6 sequence [1,1,1,1,1,-5,...].
Expansion of eta(q^6)^6/(eta(q)q^(35/24)) in powers of q.
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REFERENCES
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Garvan, F., Kim, D., and Stanton, D., Cranks and t-cores, Inventiones Math. 101 (1990) 1-17
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
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FORMULA
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G.f.: Product_{k>0} (1-q^(6k))^6/(1-q^k).
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(prod(k=1, n, (1-x^(6*k)+x*O(x^n))^6/(1-x^k)), n))
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff(eta(x^6+A)^6/eta(x+A), n))}
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CROSSREFS
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Cf. A010054, A033687, A045831, A053723, A053724.
Sequence in context: A103866 A080164 A126048 this_sequence A064143 A115274 A126890
Adjacent sequences: A081619 A081620 A081621 this_sequence A081623 A081624 A081625
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KEYWORD
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nonn,easy
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AUTHOR
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Michael Somos, Mar 24, 2003
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