OFFSET
0,6
REFERENCES
S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 41, 13th equation.
FORMULA
EXAMPLE
G.f. = 1 - x^3 + x^4 - 2*x^5 + 2*x^6 - 3*x^7 + 4*x^8 - 5*x^9 + 6*x^10 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QHypergeometricPFQ[ {x}, {x^2}, x^2, x^3], {x, 0, n}]; (* Michael Somos, Sep 07 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( sum(k=0, n, if( issquare( 3*k + 1, &m), (-1)^(m \ 3) * x^k ), A) / sum(k=0, (sqrtint(8*n + 1) - 1) \ 2, x^((k^2 + k) / 2), A), n))};
(PARI) {a(n) = if( n<0, 0, polcoeff( sum(k=0, sqrtint(n+1) - 1, (-1)^k * x^(k^2 + 2*k) * prod(j=1, k, (1 - x^(2*j - 1)) / (1 - x^(2*j))^2, 1 + O(x^(n + 1 - k^2 - 2*k)))), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Jul 21 2008
STATUS
approved