A186001 Expansion of 1/(1-x/(1-x/(1-x/(1-2x/(1-x/(1-4x/(1-x/(1-6x/(1-... (continued fraction).

1, 1, 2, 5, 15, 52, 205, 917, 4658, 26817, 173899, 1257916, 10036409, 87351977, 821268402, 8273013085, 88696718215, 1006586902196, 12037812901733, 151136735414301, 1985815346287906

Offset: 0

Author

Paul Barry, Feb 09 2011

Keywords

• nonn
• easy

Comments

Hankel transform is A186002.

Crossrefs

Cf. A004211, A186002.

Formula

G.f.: 1/(1-x/(1-x*g(x))), g(x) the g.f. of A004211.

G.f.: 1/(1-x-x^2/(1-2x-2x^2/(1-3x-4x^2/(1-5x-6x^2/(1-7x-8x^2/(1-.... (continued fraction).

a(n) = a(n-1) + Sum_{i=0..n-2} A004211(i)*a(n-1-i) for n > 0.