A106181 Expansion of c(-x^2)(1+2x-sqrt(1+4x^2))/2, c(x) the g.f. of A000108.

0, 1, -1, -1, 2, 2, -5, -5, 14, 14, -42, -42, 132, 132, -429, -429, 1430, 1430, -4862, -4862, 16796, 16796, -58786, -58786, 208012, 208012, -742900, -742900, 2674440, 2674440, -9694845, -9694845, 35357670, 35357670, -129644790, -129644790, 477638700, 477638700, -1767263190, -1767263190

Offset

0,5

Comments

Second column of number triangle A106180.

Links

Table of n, a(n) for n=0..39.

Formula

a(n) = sin(Pi*n/2)*(C((n-1)/2)*(1-(-1)^n)/2) + sin(Pi*(n+1)/2)*(C(n/2)*(1+(-1)^n)/2) - 0^n for n > 0.

Conjecture: (n+2)*a(n) + n*a(n-1) + 4*(n-1)*a(n-2) + 4*(n-3)*a(n-3) = 0. - R. J. Mathar, Nov 15 2011

Crossrefs

Cf. A000108, A099363.

Sequence in context: A129996 A208355 A099363 * A098887 A259097 A245845

Adjacent sequences: A106178 A106179 A106180 * A106182 A106183 A106184

Keyword

easy,sign

Author

Paul Barry, Apr 24 2005

Status

approved