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 A264136 Expansion of f(-q) * phi(q) in powers of q where f() is a Ramanujan theta function and phi() is a 6th-order mock theta function. 1
 1, -2, 2, -2, 0, -2, 4, 0, 2, -2, 2, -4, -2, 0, 6, -2, 0, -4, 4, 0, -2, -2, 2, -4, 2, 2, 8, -2, -2, -4, 2, 0, 2, -2, 0, -4, -2, 0, 8, -2, 0, -4, 6, 0, -2, 0, 0, -4, 0, -2, 6, -2, -2, -4, 4, 2, 6, 0, 0, -4, -2, 0, 8, -4, 0, -2, 2, 0, -2, -4, -2, -4, 4, 0, 8, 2 (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 OFFSET 0,2 REFERENCES Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 2, 2nd equation. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..1000 (corrected previous b-file from G. C. Greubel) FORMULA Convolution of A010815 and A053268. G.f.: Sum_{k in Z} x^(6*k^2 + k) / (1 - x^k + x^(2*k)) - 2 * Sum_{k in Z} x^(6*k^2 - 2*k) / (1 + x^(3*k - 1)). EXAMPLE G.f. = 1 - 2*x + 2*x^2 - 2*x^3 - 2*x^5 + 4*x^6 + 2*x^8 - 2*x^9 + 2*x^10 - 4*x^11 + ... MATHEMATICA a[ n_] := If[ n < 0, 0, SeriesCoefficient[ QPochhammer[ x] Sum[ (-1)^k x^k^2 QPochhammer[ x, x^2, k] / QPochhammer[ -x, x, 2*k], {k, 0, Sqrt@n}], {x, 0, n}]]; nmax = 122; CoefficientList[Series[QPochhammer[q]*Sum[(-1)^n*q^n^2*Product[1 - q^k, {k, 1, 2*n - 1, 2}] / Product[1 + q^k, {k, 1, 2*n}], {n, 0, Floor[Sqrt[nmax]]}], {q, 0, nmax}], q] (* G. C. Greubel, Mar 18 2018, fixed by Vaclav Kotesovec, Jun 15 2019 *) PROG (PARI) {a(n) = if( n<0, 0, polcoeff( eta(x + x * O(x^n)) * sum(k=0, sqrtint(n), (-1)^k * x^k^2 * prod(i=1, k, 1 - x^(2*i - 1), 1 + x * O(x^(n - k^2))) / prod(i=1, 2*k, 1 + x^i, 1 + x * O(x^(n - k^2))) ), n))}; CROSSREFS Cf. A010815, A053268. Sequence in context: A336694 A130277 A109135 * A274850 A349437 A215594 Adjacent sequences: A264133 A264134 A264135 * A264137 A264138 A264139 KEYWORD sign AUTHOR Michael Somos, Nov 03 2015 STATUS approved

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Last modified July 13 02:50 EDT 2024. Contains 374265 sequences. (Running on oeis4.)