OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
FORMULA
Euler transform of period 3 sequence [ 4, 4, 1, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (576 t)) = 648^(-1/2) (t/i)^(-1/2) g(t) where q = exp(2 Pi i t) and g() is g.f. for A187427.
G.f.: Product_{k>0} (1 - x^(3*k))^3 / (1 - x^k)^4.
a(n) ~ exp(sqrt(2*n)*Pi)/(12*sqrt(3)*n). - Vaclav Kotesovec, Sep 07 2015
EXAMPLE
1 + 4*x + 14*x^2 + 37*x^3 + 93*x^4 + 210*x^5 + 454*x^6 + 925*x^7 + ...
q^5 + 4*q^29 + 14*q^53 + 37*q^77 + 93*q^101 + 210*q^125 + 454*q^149 + ...
MATHEMATICA
nmax = 40; CoefficientList[Series[Product[(1 - x^(3*k))^3 / (1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 07 2015 *)
eta[q_] := q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-5/24) *eta[q^3]^3/eta[q]^4, {q, 0, 50}], q] (* G. C. Greubel, Aug 14 2018 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^3 + A)^3 / eta(x + A)^4, n))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Mar 09 2011
STATUS
approved