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A123655
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Expansion of q*psi(q^8)/phi(-q) in powers of q where psi(),phi() are Ramanujan theta functions.
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1
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1, 2, 4, 8, 14, 24, 40, 64, 101, 156, 236, 352, 518, 752, 1080, 1536, 2162, 3018, 4180, 5744, 7840, 10632, 14328, 19200, 25591, 33932, 44776, 58816, 76918, 100176, 129952, 167936, 216240, 277476, 354864, 452392, 574958, 728568, 920600, 1160064
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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
| Expansion of eta(q^2)eta(q^16)^2/(eta(q)^2*eta(q^8)) in powers of q.
Euler transform of period 16 sequence [ 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= u^2 -v*(1+4*u+2*v+8*u*v)
a(n) is odd iff n is an odd square. If n>2 is a power of 2 then the highest power of 2 dividing a(n) is (n/2)^3. - Michael Somos Feb 18 2007
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PROG
| (PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^16+A)^2/eta(x+A)^2/eta(x^8+A), n))}
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CROSSREFS
| A007096(n)=4*a(n) if n>0.
Sequence in context: A069253 A004402 A015128 * A084683 A118544 A019274
Adjacent sequences: A123652 A123653 A123654 * A123656 A123657 A123658
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Oct 04 2006
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