OFFSET
0,3
COMMENTS
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)
F. Garvan, D. Kim and D. Stanton, Cranks and t-cores, Inventiones Math. 101 (1990) 1-17.
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of f(-x^11)^11 / f(-x) in powers of x where f() is a Ramanujan theta function.
Expansion of q^-5 * etq(q^11)^11 / eta(q) in powers of q. - Michael Somos, Nov 06 2014
Euler transform of period 11 sequence [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -10, ...]. - Michael Somos, Nov 06 2014
G.f. Product_{k>0} (1 - x^(11*k))^11 / (1 - x^k).
EXAMPLE
G.f. = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 7*x^5 + 11*x^6 + 15*x^7 + 22*x^8 + ...
G.f. = q^5 + q^6 + 2*q^7 + 3*q^8 + 5*q^9 + 7*q^10 + 11*q^11 + 15*q^12 + ...
MATHEMATICA
m = 50; CoefficientList[ Series[ Product[(1-q^(11*k))^11/(1-q^k), {k, 1, m}], {q, 0, m}], q] (* Jean-François Alcover, Jul 26 2011, after g.f. *)
a[ n_] := SeriesCoefficient[ QPochhammer[ x^11]^11 / QPochhammer[ x], {x, 0, n}]; (* Michael Somos, Nov 06 2014 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^11 + A)^11 / eta(x + A), n))}; /* Michael Somos, Nov 06 2014 */
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
James A. Sellers, Feb 14 2000
STATUS
approved