OFFSET
0,2
COMMENTS
Euler transform of period 4 sequence [4,-8,4,-3,...].
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: Product_{n>0} (1-x^(2n))^12/((1-x^n)^4(1-x^(4n))^5).
MAPLE
with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add([-3, 4, -8, 4]
[1+irem(d, 4)]*d, d=divisors(j)) *a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..100); # Alois P. Heinz, Mar 05 2015
MATHEMATICA
a[n_] := a[n] = If[n==0, 1, Sum[DivisorSum[j, {-3, 4, -8, 4}[[1 + Mod[#, 4]]]*#&]*a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Nov 25 2015, after Alois P. Heinz *)
PROG
(PARI) a(n)=local(X); if(n<0, 0, X=x+x*O(x^n); polcoeff(eta(X)^-4*eta(X^2)^12*eta(X^4)^-5, n))
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Feb 28 2003
STATUS
approved