This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A228447 Expansion of q * (psi(q^3) * psi(q^6)) / (psi(q) * phi(q)) in powers of q where phi(), psi() are Ramanujan theta functions. 5
 1, -3, 7, -15, 30, -57, 104, -183, 313, -522, 852, -1365, 2150, -3336, 5106, -7719, 11538, -17067, 25004, -36306, 52280, -74700, 105960, -149277, 208951, -290706, 402127, -553224, 757158, -1031166, 1397744, -1886151, 2534316, -3391254, 4520112, -6002007 (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 G. C. Greubel, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of q * (psi(q^3)^3 / psi(q)) / (phi(q) * phi(q^3)) in powers of q where phi(), psi() are Ramanujan theta functions. Expansion of eta(q)^3 * eta(x^4)^2 * eta(x^6) * eta(x^12)^2 / (eta(x^2)^7 * eta(x^3)) in powers of q. G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^2 * (1 - 3*v) - v * (1 - 4*v) * (1 - 3*u)^2. a(n) = -(-1)^n * A187100(n). a(2*n) = -3 * A128638(n). Convolution inverse is A187145. Convolution with A033716 is A093829. EXAMPLE G.f. = q - 3*q^2 + 7*q^3 - 15*q^4 + 30*q^5 - 57*q^6 + 104*q^7 - 183*q^8 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ (1/4) EllipticTheta[ 2, 0, q^(3/2)]^3 / (EllipticTheta[ 2, 0, q^(1/2)] EllipticTheta[ 3, 0, q] EllipticTheta[ 3, 0, q^3]), {q, 0, n}] PROG (PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x + A)^3 * eta(x^4 + A)^2 * eta(x^6 + A) * eta(x^12 + A)^2 / (eta(x^2 + A)^7 * eta(x^3 + A)), n))} CROSSREFS Cf. A033716, A093829, A128638, A187100, A187145. Sequence in context: A290865 A055795 A058695 * A187100 A209816 A182726 Adjacent sequences:  A228444 A228445 A228446 * A228448 A228449 A228450 KEYWORD sign AUTHOR Michael Somos, Oct 26 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 14 17:32 EST 2019. Contains 329979 sequences. (Running on oeis4.)