A258453 G.f.: Sum_{k>0} x^((k^2 + k)/2) / (1 + x^k).

1, -1, 2, -1, 0, 0, 2, -1, -1, 0, 2, 0, 0, -2, 2, -1, 0, 1, 2, -2, 0, -2, 2, 0, 1, 0, 0, 0, 0, -2, 2, -1, 0, 0, 2, 1, 0, -2, 0, -2, 0, 2, 2, -2, 2, -2, 2, 0, -1, -1, 0, 0, 0, -2, 4, 0, 0, 0, 2, -2, 0, -2, 0, -1, 0, 2, 2, 0, 0, -2, 2, -1, 0, 0, 2, -2, -2, 0, 2

Offset: 1

Author

Michael Somos, Nov 05 2015

Keywords

• sign

Examples

			G.f. = x - x^2 + 2*x^3 - x^4 + 2*x^7 - x^8 - x^9 + 2*x^11 - 2*x^14 + 2*x^15 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A001227, A048272.

Programs

Mathematica

a[ n_] := If[ n < 0, 0, SeriesCoefficient[ Sum[ x^((k^2 + k)/2) / (1 + x^k), {k, Sqrt[8 n + 1]}], {x, 0, n}]];

PARI

{a(n) = if( n<0, 0, polcoeff( sum(k=1, sqrtint(8*n + 1), x^((k^2 + k)/2) / (1 + x^k), x * O(x^n)), n))};