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!)
 A249010 Expansion of (P(q) - 3*P(q^2) - 5*P(q^5) + 15*P(q^10)) / 8 in powers of q where P() is a Ramanujan Eisenstein series. 0
 1, -3, 0, -12, 6, -3, 0, -24, 18, -39, 0, -36, 24, -42, 0, -12, 42, -54, 0, -60, 6, -96, 0, -72, 72, -3, 0, -120, 48, -90, 0, -96, 90, -144, 0, -24, 78, -114, 0, -168, 18, -126, 0, -132, 72, -39, 0, -144, 168, -171, 0, -216, 84, -162, 0, -36, 144, -240, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Ramanujan's Eisenstein series: P(q) (see A006352), Q(q) (A004009), R(q) (A013973). LINKS Table of n, a(n) for n=0..58. FORMULA If n>0 then a(n) = -3 * b(n) where b is multiplicative with b(2^e) = 2 - 2^e, b(5^e) = 1, and b(p^e) = (p^(e+1) - 1) / (p - 1) otherwise. G.f.: 1 - 3 * Sum_{k>0} c(k) * x^k / (1 - x^k)^2 where c(k) is a period 10 integer sequence. G.f.: 1 - 3/2 * Sum_{k>0} c(k) * k * x^k / (1 - x^k) where c(k) is a period 10 integer sequence. a(4*n) = A028887(n). a(4*n + 2) = 0. EXAMPLE G.f. = 1 - 3*q - 12*q^3 + 6*q^4 - 3*q^5 - 24*q^7 + 18*q^8 - 39*q^9 + ... PROG (PARI) {a(n) = local(A, p, e); if( n<1, n==0, A = factor(n); -3 * prod( k=1, matsize(A)[1], if( p=A[k, 1], e=A[k, 2]; if( p==2, 2 - 2^e, if( p==5, 1, (p^(e+1) - 1) / (p - 1))))))}; (PARI) {a(n) = if( n<1, n==0, -3 * sumdiv(n, k, n/k * [8, 1, -2, 1, -2, -4, -2, 1, -2, 1][k%10 + 1]))}; (PARI) {a(n) = if( n<1, n==0, -3/2 * sumdiv(n, k, k * [0, 2, -1, 2, -1, 0, -1, 2, -1, 2][k%10 + 1]))}; (Magma) A := Basis( ModularForms( Gamma0(10), 2), 60); A[1] - 3*A[2]; CROSSREFS Cf. A028887. Sequence in context: A194093 A055314 A110890 * A071534 A336667 A269880 Adjacent sequences: A249007 A249008 A249009 * A249011 A249012 A249013 KEYWORD sign AUTHOR Michael Somos, Oct 18 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 May 25 16:17 EDT 2024. Contains 372801 sequences. (Running on oeis4.)