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Search: id:A137685
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| A137685 |
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Expansion of phi(-q^3) / f(-q)^2 in powers of q where phi(), f() are Ramanujan theta functions. |
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1
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| 1, 2, 5, 8, 16, 26, 45, 70, 113, 170, 261, 382, 567, 812, 1171, 1646, 2322, 3212, 4448, 6066, 8272, 11142, 14992, 19970, 26561, 35032, 46117, 60280, 78631, 101946, 131888, 169724, 217937, 278548, 355237, 451178, 571799, 722002, 909744, 1142502
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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G. E. Andrews, q-series, CBMS Regional Conference Series in Mathematics, 66, Amer. Math. Soc. 1986, see p. 71, Eq. (7.30). MR0858826 (88b:11063)
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FORMULA
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Euler transform of period 6 sequence [ 2, 2, 0, 2, 2, 1, ...].
G.f.: Product_{k>0} (1 + x^k + x^(2*k)) / ( (1 - x^(2*k)) * (1 - x^k +x^(2*k)) ).
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EXAMPLE
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1 + 2*q + 5*q^2 + 8*q^3 + 16*q^4 + 26*q^5 + 45*q^6 + 70*q^7 + 113*q^8 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( sum(k=1, sqrtint(n \ 3), 2 * (-1)^k * x^(3*k^2), 1 + A) / eta(x + A)^2, n))}
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CROSSREFS
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Sequence in context: A065093 A129299 A096541 this_sequence A093065 A026007 A032233
Adjacent sequences: A137682 A137683 A137684 this_sequence A137686 A137687 A137688
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Feb 05 2008
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