A208061 G.f. 1/sum(k>=0, (-1)^k * x^(k*(k+1)/2)).

1, 1, 1, 0, -1, -2, -1, 1, 4, 5, 2, -5, -12, -13, -3, 17, 34, 32, -1, -54, -93, -72, 28, 169, 248, 152, -147, -510, -646, -282, 582, 1484, 1627, 375, -2045, -4195, -3927, 110, 6716, 11544, 9002, -3458, -20996, -30921, -19123, 17974, 63154, 80435, 35553, -71525, -183969

Offset: 0

Author

Franklin T. Adams-Watters, Feb 23 2012

Keywords

• sign

Examples

			G.f. = 1 + x + x^2 - x^4 - 2*x^5 - x^6 + x^7 + 4*x^8 + 5*x^9 + 2*x^10 - 5*x^11 + ...
		

Crossrefs

Cf. A006950, A023361, A106507, A197870.

Programs

PARI

al(n)=Vec(1/(sum(k=0,sqrtint(2*n),(-1)^k*x^(k*(k+1)\2))+x*O(x^n)))

Formula

G.f.: 1 / (1 - x*(1 - x^2*(1 - x^3*(1 - x^4*(1 - ...))))). - Michael Somos, Mar 03 2014

Convolution inverse of A197870. - Michael Somos, Mar 03 2014