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A260164
Expansion of f(-x^8)^2 / f(-x) in powers of x where f() is a Ramanujan theta function.
1
1, 1, 2, 3, 5, 7, 11, 15, 20, 28, 38, 50, 67, 87, 113, 146, 186, 236, 299, 375, 468, 583, 721, 888, 1093, 1336, 1628, 1980, 2397, 2894, 3487, 4186, 5013, 5991, 7139, 8488, 10073, 11924, 14086, 16613, 19551, 22965, 26934, 31527, 36844, 42994, 50085, 58258
OFFSET
0,3
COMMENTS
Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
LINKS
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q^(-5/8) * eta(q^8)^2 / eta(q) in powers of q.
Euler transform of period 8 sequence [ 1, 1, 1, 1, 1, 1, 1, -1, ...].
2 * a(n) = A132965(2*n + 1).
EXAMPLE
G.f. = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 7*x^5 + 11*x^6 + 15*x^7 + 20*x^8 + ...
G.f. = q^5 + q^13 + 2*q^21 + 3*q^29 + 5*q^37 + 7*q^45 + 11*q^53 + 15*q^61 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^8]^2 / QPochhammer[ x], {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^8 + A)^2 / eta(x + A), n))};
CROSSREFS
Sequence in context: A090693 A260794 A277576 * A280938 A049756 A319472
KEYWORD
nonn
AUTHOR
Michael Somos, Nov 09 2015
STATUS
approved