VOOZH about

URL: https://oeis.org/A122928

⇱ A122928 - OEIS

login
A122928
Coefficients of a q-series inspired by Andrews and Ramanujan.
0
1, 1, 2, 3, 5, 8, 12, 18, 26, 37, 52, 72, 99, 134, 180, 240, 317, 416, 542, 702, 904, 1158, 1476, 1872, 2364, 2973, 3724, 4647, 5778, 7160, 8844, 10890, 13370, 16368, 19984, 24336, 29561, 35822, 43308, 52242, 62884, 75536, 90552, 108342, 129384, 154232
OFFSET
0,3
LINKS
G. E. Andrews, Three aspects of partitions, Séminaire Lotharingien de Combinatoire, B25f (1990), 1 p.
FORMULA
Euler transform of period 24 sequence [ 1, 1, 1, 1, 2, 1, 2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 1, 1, 1, 0, ...].
Given g.f. A(x), then B(x)=A(x)^2-A(x) satisfies 0=f(B(x), B(x^2)) where f(u, v)=(1+6*u)*v*(1+2*v)-u^2.
G.f.: {Sum_{k} q^(6k^2-k) }/{Sum_{k} (-1)^k q^((3k^2-k)/2) }.
G.f.: Product_{k>0} (1-q^(12k))(1+q^(12k-5))(1+q^(12k-7))/(1-q^k).
G.f.: 1+Sum_{k>0} Prod[i=1..k, (1+q^i)^2]*(1+q^k)*q^(k^2) /{(1-q)(1-q^2)...(1-q^(2k))}.
a(n) ~ exp(Pi*sqrt(2*n/3)) / (2^(9/4) * 3^(3/4) * n^(3/4)). - Vaclav Kotesovec, Aug 31 2015
MATHEMATICA
nmax = 100; CoefficientList[Series[Product[(1-x^(12*k))*(1+x^(12*k-5))*(1+x^(12*k-7))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 31 2015 *)
PROG
(PARI) {a(n)=if(n<1, n==0, polcoeff( sum(k=1, sqrtint(n), x^k^2/(1+x^k)* prod(i=1, k, (1+x^i)^2/(1-x^(2*i-1))/(1-x^(2*i)), 1+x*O(x^(n-k^2)))), n))}
CROSSREFS
Cf. A098693(n)=a(n) if n>0.
Sequence in context: A058984 A084376 A098693 * A200310 A328085 A001524
KEYWORD
nonn
AUTHOR
Michael Somos, Sep 19 2006
STATUS
approved