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A132212
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Expansion of f(-q, -q^7)/ phi(-q) in powers of q where f(), phi() are Ramanujan theta functions.
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1, 1, 2, 4, 6, 10, 16, 23, 34, 50, 71, 100, 140, 192, 262, 356, 476, 634, 840, 1102, 1440, 1872, 2417, 3108, 3980, 5070, 6434, 8135, 10242, 12852, 16076, 20036, 24898, 30852, 38112, 46958, 57708, 70730, 86486, 105508, 128412, 155952, 189004, 228580
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| Euler transform of period 8 sequence [ 1, 1, 2, 1, 2, 1, 1, 0, ...].
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PROG
| (PARI) {a(n)= if(n<0, 0, polcoeff( prod(k=1, n, 1/(1 -x^k +x*O(x^n))^[0, 1, 1, 2, 1, 2, 1, 1][k%8+1]), n))}
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CROSSREFS
| Sequence in context: A192447 A131882 A073150 * A137414 A098151 A132002
Adjacent sequences: A132209 A132210 A132211 * A132213 A132214 A132215
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Aug 13 2007
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