|
%I #4 Apr 26 2015 15:51:22
%S 1,0,1,-1,1,-1,2,-2,2,-3,4,-4,5,-6,7,-8,9,-11,13,-14,17,-20,22,-25,29,
%T -33,37,-42,48,-54,61,-68,77,-87,96,-108,122,-135,150,-168,187,-207,
%U 230,-255,283,-313,345,-382,422,-464,511,-564,620,-680,748,-821,900,-986,1079,-1182,1293,-1411,1542
%N G.f.: Product_{k>0} (1-x^(4k-1)) / (1-x^(4k-2)).
%D N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 25, Eq. (20.23).
%F Euler transform of period 4 sequence [ 0, 1, -1, 0, ...].
%F G.f.: 1 + Sum_{k>0} x^(k^2+k)*(1-x)(1-x^3)...(1-x^(2k-1))/((1-x^2)(1-x^4)...(1-x^(2k))).
%e G.f. = 1 + x^2 - x^3 + x^4 - x^5 + 2*x^6 - 2*x^7 + 2*x^8 - 3*x^9 + 4*x^10 + ...
%o (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1-x^k)^((k%4==3) - (k%4==2)), 1 + x * O(x^n)), n))};
%K sign
%O 0,7
%A _Michael Somos_, Jul 16 2007
|
