OFFSET
0,2
COMMENTS
Convolution square of A007242. - Michael Somos, Mar 31 2019
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Seiichi Manyama)
Eric Weisstein's World of Mathematics, j-Function
Wikipedia, j-invariant
FORMULA
G.f.: Product_{k>=1} (1-q^k)^A289061(k).
a(n) = A000521(n-1) for n = 0 and n > 1.
a(n) ~ exp(4*Pi*sqrt(n)) / (sqrt(2) * n^(3/4)). - Vaclav Kotesovec, Jul 09 2017
G.f.: q * (j(q) - 1728) where j(q) is a modular function. - Michael Somos, Mar 31 2019
EXAMPLE
G.f. = (1-q)^984 * (1-q^2)^286752 * (1-q^3)^102360024 * ...
G.f. = 1 - 984*q + 196884*q^2 + 21493760*q^3 + 864299970*q^4 + 20245856256*q^5 + ... .
MATHEMATICA
nmax = 20; CoefficientList[Series[(1 - 504*Sum[DivisorSigma[5, k]*x^k, {k, 1, nmax}])^2 / Product[(1 - x^k)^24, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 09 2017 *)
a[ n_] := SeriesCoefficient[ q Series[ 1728 (KleinInvariantJ[Log[q] / (2 Pi I)] - 1), {q, 0, n}], {q, 0, n}]; (* Michael Somos, Mar 31 2019 *)
PROG
(PARI) {a(n) = my(A, U1, U2); if( n<0, 0, A = x * O(x^n); U1 = eta(x + A)^24; U2 = eta(x^2 + A)^24; polcoeff( (U1 - 512*x * U2)^2 * (U1 + 64*x * U2) / (U1^2 * U2), n))}; /* Michael Somos, Mar 31 2019 */
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jun 23 2017
STATUS
approved