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 A093831 Expansion of q * (chi(-q) * chi(-q^5))^-4 in powers of q where chi() is a Ramanujan theta function. 3
 1, 4, 10, 24, 51, 104, 206, 384, 697, 1228, 2112, 3568, 5898, 9592, 15358, 24256, 37850, 58340, 88980, 134344, 200972, 298112, 438538, 640256, 928041, 1336104, 1911436, 2717776, 3842110, 5401784, 7555012, 10514176, 14562432, 20077672 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of (eta(q^2) * eta(q^10) / (eta(q) * eta(q^5)))^4 in powers of q. Euler transform of period 10 sequence [ 4, 0, 4, 0, 8, 0, 4, 0, 4, 0, ...]. G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^2 - v*(1 + 8*u + 16*u*v). G.f.: x * (Product_{k>0} (1 - x^(10*k - 5)) * (1 - x^(2*k - 1)))^-4. Convolution inverse of A132040. - Michael Somos, Apr 26 2015 a(n) ~ exp(2*Pi*sqrt(2*n/5)) / (16 * 2^(3/4) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2015 EXAMPLE G.f. = q + 4*q^2 + 10*q^3 + 24*q^4 + 51*q^5 + 104*q^6 + 206*q^7 + 384*q^8 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ q (QPochhammer[ -q, q] QPochhammer[ -q^5, q^5] )^4, {q, 0, n}]; (* Michael Somos, Apr 26 2015 *) nmax = 40; Rest[CoefficientList[Series[x * Product[1/((1 - x^(10*k - 5)) * (1 - x^(2*k - 1)))^4, {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Sep 07 2015 *) PROG (PARI) {a(n) = if( n<1, 0, n--; polcoeff( (1 / prod(k=1, (n+5)\10, 1 - x^(10*k - 5), 1 + x * O(x^n)) / prod(k=1, (n+1)\2, 1 - x^(2*k - 1), 1 + x * O(x^n)))^4, n))}; (PARI) {a(n) = my(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( (eta(x^2 + A) * eta(x^10 + A) / (eta(x + A) * eta(x^5 + A)))^4, n))}; CROSSREFS Cf. A132040. Sequence in context: A309777 A128516 A022569 * A274582 A052365 A107659 Adjacent sequences:  A093828 A093829 A093830 * A093832 A093833 A093834 KEYWORD nonn AUTHOR Michael Somos, Apr 17 2004, Oct 04 2004 EXTENSIONS Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 05 2007 STATUS approved

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Last modified September 18 16:55 EDT 2020. Contains 337170 sequences. (Running on oeis4.)