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 A081622 Number of 6-core partitions of n. 4
 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; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Euler transform of period 6 sequence [ 1, 1, 1, 1, 1, -5, ...]. Expansion of q^(-35/24) * eta(q^6)^6 / eta(q) in powers of q. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe) F. Garvan, D. Kim and D. Stanton, Cranks and t-cores, Inventiones Math. 101 (1990) 1-17. FORMULA G.f.: Product_{k>0} (1 - x^(6*k))^6 / (1 - x^k). EXAMPLE 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 7*x^5 + 5*x^6 + 9*x^7 + 10*x^8 + 12*x^9 + ... q^35 + q^59 + 2*q^83 + 3*q^107 + 5*q^131 + 7*q^155 + 5*q^179 + 9*q^203 + ... PROG (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))} CROSSREFS Cf. A010054, A033687, A045831, A053723, A053724. Sequence in context: A234316 A284630 A345872 * A064143 A283593 A115274 Adjacent sequences: A081619 A081620 A081621 * A081623 A081624 A081625 KEYWORD nonn,easy AUTHOR Michael Somos, Mar 24 2003 STATUS approved

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Last modified December 1 23:44 EST 2022. Contains 358485 sequences. (Running on oeis4.)