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A185220 Expansion of phi(x^3) * psi(x)^2 / chi(-x) in powers of x where phi(), psi(), chi() are Ramanujan theta functions. 3
1, 3, 4, 5, 5, 5, 7, 7, 9, 7, 6, 11, 8, 10, 8, 9, 14, 10, 15, 7, 7, 14, 14, 16, 8, 13, 13, 12, 18, 14, 13, 15, 15, 16, 9, 11, 22, 16, 19, 16, 11, 17, 16, 23, 19, 9, 22, 18, 16, 15, 18, 27, 12, 23, 11, 15, 24, 24, 27, 9, 23, 23, 20, 21, 19, 15, 22, 24, 22, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-7/24) * eta(q^2)^5 * eta(q^3)^2 / (eta(q)^3 * eta(q^6)) in powers of q.

Euler transform of period 6 sequence [ 3, -2, 1, -2, 3, -3, ...].

G.f.: Product_{k>0} (1 - x^k)^2 * (1 + x^k)^5 * (1 - x^(3*k)) / (1 + x^(3*k)).

a(n) = A224825(3*n) = A227595(3*n).

EXAMPLE

1 + 3*x + 4*x^2 + 5*x^3 + 5*x^4 + 5*x^5 + 7*x^6 + 7*x^7 + 9*x^8 + 7*x^9 + ...

q^7 + 3*q^31 + 4*q^55 + 5*q^79 + 5*q^103 + 5*q^127 + 7*q^151 + 7*q^175 + ...

MATHEMATICA

nmax = 100; CoefficientList[Series[Product[(1 - x^k)^2 * (1 + x^k)^5 * (1 - x^(3*k)) / (1 + x^(3*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 08 2015 *)

PROG

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^5 * eta(x^3 + A)^2 / (eta(x + A)^3 * eta(x^6 + A)), n))}

CROSSREFS

Cf. A224825, A227595.

Sequence in context: A073169 A166268 A239669 * A120677 A266898 A098200

Adjacent sequences:  A185217 A185218 A185219 * A185221 A185222 A185223

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 29 2013

STATUS

approved

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Last modified June 22 09:57 EDT 2021. Contains 345375 sequences. (Running on oeis4.)