login
A260165
Expansion of f(x, x^2) * f(x, x^3)^3 in powers of x where f(, ) is Ramanujan's general theta function.
2
1, 4, 7, 10, 13, 14, 18, 22, 25, 28, 26, 34, 37, 36, 43, 38, 49, 54, 56, 58, 43, 64, 67, 70, 73, 62, 79, 72, 90, 88, 74, 98, 97, 100, 90, 84, 108, 112, 115, 126, 98, 108, 127, 130, 140, 110, 139, 142, 126, 148, 133, 154, 152, 160, 163, 108, 169, 182, 175, 180
OFFSET
0,2
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 phi(-x^3) * f(-x^2)^5 / phi(-x)^2 in powers of x where phi(), f() are Ramanujan theta functions.
Expansion of q^(-5/12) * eta(q^2)^7 * eta(q^3)^2 / (eta(q)^4 * eta(q^6)) in powers of q.
Euler transform of period 6 sequence [4, -3, 2, -3, 4, -4, ...].
a(n) = A260158(2*n).
EXAMPLE
G.f. = 1 + 4*x + 7*x^2 + 10*x^3 + 13*x^4 + 14*x^5 + 18*x^6 + 22*x^7 + 25*x^8 + ...
G.f. = q^5 + 4*q^17 + 7*q^29 + 10*q^41 + 13*q^53 + 14*q^65 + 18*q^77 + 22*q^89 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^3] QPochhammer[ x^2]^5 / EllipticTheta[ 4, 0, x]^2, {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^7 * eta(x^3 + A)^2 / (eta(x + A)^4 * eta(x^6 + A)), n))};
CROSSREFS
Cf. A260158.
Sequence in context: A331207 A090384 A327422 * A055054 A196415 A186327
KEYWORD
nonn
AUTHOR
Michael Somos, Nov 09 2015
STATUS
approved