The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A234565 Expansion of f(-q^3)^2 * Q(q^3) + 48 * q * f(-q^3)^10 in powers of q. 2
 1, 48, 0, 238, -480, 0, 1679, 1680, 0, 2162, -1440, 0, 2401, -5040, 0, -6958, 11424, 0, -1442, 0, 0, -23040, -12480, 0, 1918, -7920, 0, -9362, 6720, 0, 14641, 50592, 0, 0, -36960, 0, 80640, -28560, 0, -20398, 0, 0, 28083, -34320, 0, 64078, 103776, 0, -38398 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS f(-q) (g.f. A010815) and Q(q) (g.f. A004009) are Ramanujan q-series. LINKS G. C. Greubel, Table of n, a(n) for n = 0..2500 FORMULA G.f. is a period 1 Fourier series which satisfies f(-1 / (144 t)) = 12^5 (t/i)^5 f(t) where q = exp(2 Pi i t). a(n) = b(4*n + 1) where b() is multiplicative with b(2^e) = b(3^e) = 0^e, b(p^e) = (1 + (-1)^e) / 2 * p^(2*e) if p == 7 or 11 (mod 12), b(p^e) = b(p) * b(p^(e-1)) - p^4 * b(p^(e-2)) if p == 1 or 5 (mod 12). a(3*n + 2) = 0. a(3*n) = A122266(n). a(3*n + 1) = 48 * A010818(n). EXAMPLE G.f. = 1 + 48*x + 238*x^3 - 480*x^4 + 1679*x^6 + 1680*x^7 + 2162*x^9 + ... G.f. = q + 48*q^5 + 238*q^13 - 480*q^17 + 1679*q^25 + 1680*q^29 + 2162*q^37 + ... MATHEMATICA eta[q_]:= q^(1/24)*QPochhammer[q]; Q:= (eta[q^3]^24 + 256*eta[q^6]^24)/( eta[q^3]*eta[q^6])^8; a:= CoefficientList[Series[q^(-1/4)*eta[q^3]^2*(48*q^(0/4)*eta[q^3]^8 + Q), {q, 0, 55}], q]]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Aug 07 2018 *) PROG (PARI) {a(n) = local(A, B); if( n<0, 0, A = x * O(x^n); B = 64 * x^3 * (eta(x^12 + A) / eta(x^3 + A))^8; polcoeff( 48 * x * eta(x^3 + A)^10 + (1 + 4*B + B^2) * eta(x^3 + A)^18 / eta(x^6 + A)^8, n))} (PARI) {a(n) = local(A, p, e, i, x, y, a0, a1); if( n<0, 0, n = 4*n + 1; A = factor(n); prod( k=1, matsize(A)[1], if( p=A[k, 1], e=A[k, 2]; if( p<5, 0, if( p%12 > 6, if( e%2, 0, p^(2*e)), forstep( i = 1, sqrtint( p), 2, if( issquare( p - i^2, &y), x=i; break)); if( p%12 == 5, a1 = 8 * x*y * (x-y) * (x+y) * (-1)^((x%6==1) + (y%6==4)), a1 = 2 * (x^2-y^2+2*x*y) * (x^2-y^2-2*x*y) * (-1)^(x%6==3) ); a0 = 1; y = a1; for( i=2, e, x = y * a1 - p^4 * a0; a0=a1; a1=x); a1 )))))} CROSSREFS Cf. A010818, A122266. Sequence in context: A271194 A002834 A057380 * A362715 A036210 A257875 Adjacent sequences: A234562 A234563 A234564 * A234566 A234567 A234568 KEYWORD sign AUTHOR Michael Somos, Jan 06 2014 STATUS approved

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

Last modified June 19 02:16 EDT 2024. Contains 373492 sequences. (Running on oeis4.)