OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
M. D. Hirschhorn and J. A. Sellers, Arithmetic properties of partitions with odd parts distinct, Ramanujan J. 22 (2010), 273--284.
L. Wang, Arithmetic properties of partition triples with odd parts distinct, Int. J. Number Theory, 11 (2015), 1791--1805.
L. Wang, Arithmetic properties of partition quadruples with odd parts distinct, Bull. Aust. Math. Soc., doi:10.1017/S0004972715000647.
L. Wang, New congruences for partitions where the odd parts are distinct, J. Integer Seq. (2015), article 15.4.2.
FORMULA
G.f.: Product_{k>=1} (1 + x^k)^4 / (1 - x^(4*k))^4, corrected by Vaclav Kotesovec, Mar 25 2017
Expansion of 1 / psi(-x)^4 in powers of x where psi() is a Ramanujan theta function.
a(n) ~ exp(sqrt(2*n)*Pi) / (2^(9/4)*n^(7/4)). - Vaclav Kotesovec, Mar 25 2017
MAPLE
Digits:=200:with(PolynomialTools): with(qseries): with(ListTools):
GenFun:=series(etaq(q, 2, 1000)^4/etaq(q, 1, 1000)^4/etaq(q, 4, 1000)^4, q, 50):
CoefficientList(sort(convert(GenFun, polynom), q, ascending), q);
MATHEMATICA
nmax = 30; CoefficientList[Series[Product[(1 + x^k)^4 / (1 - x^(4*k))^4, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 25 2017 *)
CoefficientList[Series[1/(QPochhammer[q, -q]*QPochhammer[q^2, q^2])^4, {q, 0, 50}], q] (* G. C. Greubel, Apr 17 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
M.S. Mahadeva Naika, May 18 2016
EXTENSIONS
Edited by N. J. A. Sloane, May 26 2016
STATUS
approved