login
A213617
Expansion of psi(x) * f(-x^3)^3 in powers of x where psi() and f() are Ramanujan theta functions.
5
1, 2, 3, 3, 3, 5, 4, 5, 4, 5, 7, 5, 8, 4, 5, 8, 8, 9, 5, 7, 9, 6, 9, 9, 7, 10, 10, 11, 5, 6, 12, 12, 10, 10, 7, 10, 12, 14, 10, 5, 15, 8, 13, 8, 12, 17, 10, 16, 7, 9, 14, 12, 15, 11, 11, 12, 12, 16, 14, 15, 13, 15, 13, 7, 12, 17, 16, 15, 10, 13, 18, 16, 20
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 q^(-11/24) * eta(q^2)^2 * eta(q^3)^3 / eta(q)^2 in powers of q.
Euler transform of period 6 sequence [ 2, 0, -1, 0, 2, -3, ...].
6 * a(n) = A213618(24*n + 11).
EXAMPLE
G.f. = 1 + 2*x + 3*x^2 + 3*x^3 + 3*x^4 + 5*x^5 + 4*x^6 + 5*x^7 + 4*x^8 + 5*x^9 + ...
G.f. = q^11 + 2*q^35 + 3*q^59 + 3*q^83 + 3*q^107 + 5*q^131 + 4*q^155 + 5*q^179 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^2]^2 QPochhammer[ x^3]^3 / QPochhammer[x]^2, {x, 0, n}]; (* Michael Somos, Apr 26 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A)^3 / eta(x + A)^2, n))};
CROSSREFS
Cf. A213618.
Sequence in context: A102601 A092308 A205394 * A205778 A328972 A081831
KEYWORD
nonn
AUTHOR
Michael Somos, Jun 16 2012
STATUS
approved