A106181 - OEIS

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

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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.