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 A259771 Expansion of x * psi(x^5) * f(-x^10) / f(-x^2,-x^8) in powers of x where psi(), f() are Ramanujan theta functions. 1
 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 3, 4, 4, 5, 4, 6, 5, 7, 7, 9, 8, 10, 10, 12, 12, 15, 14, 18, 17, 20, 20, 24, 24, 28, 28, 33, 33, 38, 38, 44, 45, 50, 52, 59, 60, 68, 69, 78, 80, 89, 92, 102, 105, 116, 120, 133, 137, 151, 156, 171, 178, 194, 201 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). The g.f. for this sequence is the last term of the 14th equation on page 20 of Ramanujan 1988. REFERENCES Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 20 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Euler transform of period 10 sequence [ 0, 1, 0, 0, 1, 0, 0, 1, 0, -1, ...]. a(n) = A053265(n-1) - A053267(n). EXAMPLE G.f. = x + x^3 + x^5 + x^6 + x^7 + x^8 + 2*x^9 + x^10 + 2*x^11 + x^12 + ... G.f. = q^49 + q^289 + q^529 + q^649 + q^769 + q^889 + 2*q^1009 + q^1129 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ x Product[ (1 - x^k)^{ 0, -1, 0, 0, -1, 0, 0, -1, 0, 1}[[Mod[k, 10, 1]]], {k, n}], {x, 0, n}]; QP:= QPochhammer; a[n_]:= SeriesCoefficient[ x*QP[x^10]/(QP[x^5, x^10]* QP[x^2, x^10]*QP[x^8, x^10]), {x, 0, n}]; Table[a[n], {n, 1, 100}] (* G. C. Greubel, Mar 16 2018 *) PROG (PARI) {a(n) = if( n<1, 0, n--; polcoeff( prod(k=1, n, (1 - x^k + x * O(x^n))^[ 1, 0, -1, 0, 0, -1, 0, 0, -1, 0][k%10 + 1]), n))}; CROSSREFS Cf. A053265, A053267. Sequence in context: A212813 A112219 A035458 * A194902 A194874 A194835 Adjacent sequences:  A259768 A259769 A259770 * A259772 A259773 A259774 KEYWORD nonn AUTHOR Michael Somos, Jul 04 2015 STATUS approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)