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 A279715 Expansion of a q-series used by Ramanujan in his Lost Notebook. 2
 1, 2, 4, 6, 10, 16, 23, 34, 50, 70, 98, 136, 184, 250, 336, 444, 586, 768, 997, 1290, 1660, 2120, 2698, 3420, 4310, 5414, 6776, 8442, 10488, 12986, 16020, 19710, 24180, 29574, 36082, 43910, 53293, 64538, 77980, 94000, 113082, 135760, 162648, 194502, 232164 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, page 1, 1st equation with a=1.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..1000 FORMULA G.f.: Sum_{k>=0} x^k * (1 + x) * (1 + x^2) * ... * (1 + x^k) / ((1 - x) * (1 - x^3) * ... * (1 - x^(2*k+1))). EXAMPLE G.f. = 1 + 2*x + 4*x^2 + 6*x^3 + 10*x^4 + 16*x^5 + 23*x^6 + 34*x^7 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ Sum[ x^k QPochhammer[ -x, x, k] / QPochhammer[ x, x^2, k + 1] // FunctionExpand, {k, 0, n}], {x, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( sum(k=0, n, x^k * prod(i=1, k, 1 + x^i, 1 + A) / prod(i=1, k+1, 1 - x^(2*i-1), 1 + A), A), n))}; (Magma) m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&+[x^k* (&*[(1+x^j): j in [0..k]])/(&*[(1-x^(2*s+1)): s in [0..k]]) : k in [0..(m+2)]])/2 )); // G. C. Greubel, Nov 12 2018 CROSSREFS Cf. A256209. Sequence in context: A073150 A076529 A323283 * A132212 A327047 A332281 Adjacent sequences: A279712 A279713 A279714 * A279716 A279717 A279718 KEYWORD nonn AUTHOR Michael Somos, Dec 17 2016 STATUS approved

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Last modified April 1 22:19 EDT 2023. Contains 361716 sequences. (Running on oeis4.)