OFFSET
0,2
REFERENCES
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, page 1, 1st equation with a=-1.
LINKS
Robert Israel, Table of n, a(n) for n = 0..1000
FORMULA
EXAMPLE
G.f. = 1 + 2*x + 2*x^2 + 3*x^3 + 4*x^4 + 4*x^5 + 6*x^6 + 8*x^7 + 8*x^8 + ...
MAPLE
N:= 200: # to get a(0)..a(N)
g143064:= add(x^k/mul(1+x^(2*j+1), j=0..k), k=0..2*N):
g000009:= mul(1+x^(2*k), k=1..N):
S:= series(g143064*g000009, x, 2*N+2):
seq(coeff(S, x, 2*j), j=0..N); # Robert Israel, Sep 17 2017
MATHEMATICA
a[ n_] := If[ n < 0, 0, SeriesCoefficient[ QPochhammer[ x^2] / QPochhammer[ x] Sum[ (-1)^k x^(3 k^2 + 2 k) (1 + x^(2 k + 1)), {k, 0, Sqrt[n / 3]}], {x, 0, n}]];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) / eta(x + A) * sum(k=0, sqrtint(n \ 3), (-1)^k * x^(3*k^2 + 2*k) * (1 + x^(2*k + 1)), A), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Sep 16 2017
STATUS
approved