A292445 - OEIS

%I #14 Jul 27 2018 20:36:57

%S 1,4,10,22,44,82,145,248,410,658,1036,1598,2420,3614,5322,7738,11132,

%T 15850,22353,31260,43366,59708,81650,110932,149788,201112,268562,

%U 356790,471732,620834,813480,1061496,1379626,1786282,2304440,2962566,3795921,4848160

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

%C Similar to A292420 but with a=1.

%D Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, page 1, 1st equation with a=1.

%H G. C. Greubel, <a href="/A292445/b292445.txt">Table of n, a(n) for n = 0..2500</a>

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

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

%e G.f. = 1 + 4*x + 10*x^2 + 22*x^3 + 44*x^4 + 82*x^5 + 145*x^6 + ...

%t 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}];

%o (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))};

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

%K nonn

%O 0,2

%A _Michael Somos_, Sep 16 2017