OFFSET
1,15
REFERENCES
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 41
G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part I, Springer, New York, 2005, MR2135178 (2005m:11001) See p. 235, Entry 9.4.8.
FORMULA
G.f.: x^3 / (1 - x^4) + x^8 / ((1 - x^2) * (1 - x^8)) + x^15 / ((1 - x^2) * (1 - x^4) * (1 - x^12)) + x^24 / ((1 - x^2) * (1 - x^4) * (1 - x^6) * (1 - x^16)) + ... [Ramanujan]. - Michael Somos, Jul 21 2008
2 * a(n) = A143063(n) unless n=0. - Michael Somos, Jul 09 2015
EXAMPLE
G.f. = x^3 + x^7 + x^8 + x^10 + x^11 + x^12 + x^14 + 2*x^15 + 2*x^16 + x^17 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (QHypergeometricPFQ[ {-1}, {-x^2}, x^2, -x^3] - 1) / 2, {x, 0, n}]; (* Michael Somos, Jun 25 2015 *)
PROG
(PARI) {a(n) = if( n<1, 0, polcoeff( sum(k=1, sqrtint(n+1) - 1, x^(k^2 + 2*k) / (1 - x^(4*k)) / prod(j=1, k-1, 1 - x^(2*j), 1 + O(x^(n + 1 - k^2 - 2*k)))), n))}; /* Michael Somos, Jul 21 2008 */
(PARI) {a(n) = my(A, B); if( n<1, 0, A = partitions(n); sum(k=1, length(A), if( ((B = A[k])[1])%4 == 3, prod(j=2, length(B), (B[j] > B[j-1]) && ((B[j] - B[j-1])%2 == 0)))))}; /* Michael Somos, Jul 21 2008 */
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved