A292445 Expansion of a q-series used by Ramanujan in his Lost Notebook.

1, 4, 10, 22, 44, 82, 145, 248, 410, 658, 1036, 1598, 2420, 3614, 5322, 7738, 11132, 15850, 22353, 31260, 43366, 59708, 81650, 110932, 149788, 201112, 268562, 356790, 471732, 620834, 813480, 1061496, 1379626, 1786282, 2304440, 2962566, 3795921, 4848160

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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, page 1, 1st equation with a=1.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

Formula

a(n) = 2 * A256209(n) - A279715(n).

G.f. is the product of the g.f. of A022567 and A053253.

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

Cf. A022567, A053253, A256209, A279715, A292420.

Sequence in context: A048574 A052837 A052821 * A023628 A294683 A265051

Adjacent sequences: A292442 A292443 A292444 * A292446 A292447 A292448

Keyword

nonn

Author

Michael Somos, Sep 16 2017

Status

approved