A246432 Convolution inverse of A001700.

1, -3, -1, -2, -5, -14, -42, -132, -429, -1430, -4862, -16796, -58786, -208012, -742900, -2674440, -9694845, -35357670, -129644790, -477638700, -1767263190, -6564120420, -24466267020, -91482563640, -343059613650, -1289904147324, -4861946401452

Offset: 0

Author

Michael Somos, Nov 14 2014

Keywords

• sign

Examples

			G.f. = 1 - 3*x - x^2 - 2*x^3 - 5*x^4 - 14*x^5 - 42*x^6 - 132*x^7 - 429*x^8 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1660

Crossrefs

Cf. A000108, A001700, A115140, A115141.

Programs

Magma

m:=50; R:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1 +Sqrt(1-4*x))/2 -2*x)); // G. C. Greubel, Aug 04 2018

Mathematica

CoefficientList[Series[(1 +Sqrt[1-4*x])/2 -2*x, {x, 0, 50}], x] (* G. C. Greubel, Aug 04 2018 *)

PARI

{a(n) = if( n<2, (n==0) - 3*(n==1), - binomial(2*n - 2, n-1) / n)};

PARI

{a(n) = if( n<0, 0, polcoeff( (1 + sqrt(1 - 4*x + x * O(x^n))) / 2 - 2*x, n))};

Formula

G.f.: (1 + sqrt(1 - 4*x)) / 2 - 2*x.

G.f.: -2*x + 1 - x / (1 - x / (1 - x / ...)) (continued fraction).

a(n) = A115140(n) = A115141(n) for all n in Z unless n=1.

a(n) = -A000108(n-1) for all n>1.