A131795 G.f.: Product_{k>0} (1-x^(4k-1)) / (1-x^(4k-2)).

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, -33, 37, -42, 48, -54, 61, -68, 77, -87, 96, -108, 122, -135, 150, -168, 187, -207, 230, -255, 283, -313, 345, -382, 422, -464, 511, -564, 620, -680, 748, -821, 900, -986, 1079, -1182, 1293, -1411, 1542

Offset: 0

Author

Michael Somos, Jul 16 2007

Keywords

• sign

Examples

			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 + ...
		

References

• N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 25, Eq. (20.23).

Programs

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))};

Formula

Euler transform of period 4 sequence [ 0, 1, -1, 0, ...].

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))).