A115138 A sequence related to Catalan numbers A000108.

1, -1, 1, 15, 113, 783, 5361, 36879, 255985, 1794063, 12689393, 90505231, 650379249, 4705157135, 34244198385, 250572963855, 1842382110705, 13605619630095, 100872203796465, 750556607938575, 5602962592235505, 41952165966643215, 314983352736153585

Offset: 0

Author

Wolfdieter Lang, Jan 13 2006

Keywords

• sign
• easy

Comments

See also A115150, the third diagonal of triangle A113647 (called Y(2,1)).

Examples

			15= a(3) = A062992(3) - 4*A062992(2) = 67 - 4*13.
		

Formula

(1-4*x)*(2*c(2*x)-1)/(1+x) with c(x) g.f. of A000108 (Catalan).

a(n)= A113647(n, n-1), n>=2.

a(n)= b(n)-4*b(n-1) with b(n):=A062992(n), n>=2; a(0)=1, a(1)=-1.