The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A210656 Expansion of psi(x^3) * phi(-x)^2 / phi(-x^2) in power of x where phi(), psi() are Ramanujan theta functions. 2
 1, 8, 36, 130, 412, 1176, 3105, 7712, 18192, 41098, 89476, 188592, 386322, 771528, 1506036, 2879688, 5403628, 9966408, 18092599, 32366288, 57117660, 99526362, 171378512, 291841464, 491812740, 820684904, 1356794820, 2223458146, 3613417008, 5825889936 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..2000 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of q^(-3/4) * ( eta(q^2)^4 * eta(q^6)^2 / (eta(q)^4 * eta(q^3) * eta(q^ 4)) )^2 in powers of q. Euler transform of period 12 sequence [ 8, 0, 10, 2, 8, -2, 8, 2, 10, 0, 8, 0, ...]. A001936(9*n + 2) - A001936(n) = 4 * a(3*n). A001936(9*n + 5) = 4 * a(3*n + 1). A001936(9*n + 8) = 4 * a(3*n + 2). a(n) ~ exp(sqrt(3*n)*Pi) / (32*sqrt(2)*3^(3/4)*n^(3/4)). - Vaclav Kotesovec, Nov 16 2017 EXAMPLE 1 + 8*x + 36*x^2 + 130*x^3 + 412*x^4 + 1176*x^5 + 3105*x^6 + 7712*x^7 + ... q^3 + 8*q^7 + 36*q^11 + 130*q^15 + 412*q^19 + 1176*q^23 + 3105*q^27 + ... MATHEMATICA nmax = 30; CoefficientList[Series[Product[((1 - x^(2*k))^4 * (1 - x^(6*k))^2 / ((1 - x^k)^4 * (1 - x^(3*k)) * (1 - x^(4*k))))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 16 2017 *) PROG (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( ( eta(x^2 + A)^4 * eta(x^6 + A)^2 / (eta(x + A)^4 * eta(x^3 + A) * eta(x^ 4 + A)) )^2, n))} CROSSREFS Cf. A001936. Sequence in context: A014477 A034998 A121255 * A119767 A024208 A000427 Adjacent sequences:  A210653 A210654 A210655 * A210657 A210658 A210659 KEYWORD nonn AUTHOR Michael Somos, Mar 27 2012 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 6 04:20 EST 2021. Contains 349562 sequences. (Running on oeis4.)