OFFSET
0,2
COMMENTS
Similar to A292420 but with a=1.
REFERENCES
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, page 1, 1st equation with a=1.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
EXAMPLE
G.f. = 1 + 4*x + 10*x^2 + 22*x^3 + 44*x^4 + 82*x^5 + 145*x^6 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^2]^2 / QPochhammer[ x]^2 Sum[ x^k / Product[ 1 - x^(2 i + 1), {i, 0, k}], {k, 0, n}], {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))^2 * sum(k=0, n, x^k / prod(i=0, k, 1 - x^(2*i+1), 1 + A/x^k)), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Sep 16 2017
STATUS
approved