A171151 Expansion of (A(x)-1)/(x*A(x)), A(x) the g.f. of A004211.

1, 2, 6, 26, 142, 898, 6342, 49114, 412046, 3711746, 35660166, 363484058, 3914162830, 44370673282, 527868672582, 6572992645978, 85461951576974, 1157778354181634, 16310949128381190, 238543136307926810

Offset

0,2

Comments

Hankel transform is A108400.

Links

Table of n, a(n) for n=0..19.

Formula

G.f.: 1/(1-2x/(1-x/(1-4x/(1-x/(1-6x/(1-x/(1-8x/(1-x/(1-... (continued function).

a(n) = Sum_{k=0..n} A086329(n,k)*2^k. - Philippe Deléham, Dec 05 2009

G.f.: 1/U(0) where U(k) = 1 - x - 2*x*k + x*(2*x*k + 2*x - 1)/U(k+1); (continued fraction, Euler's 1st kind, 1-step). - Sergei N. Gladkovskii, Sep 24 2012

G.f.: 1/x - 1/( x*G(0) - 1 ) where G(k) = 1 - (4*x*k-1)/(x - x^4/(x^3 - (4*x*k-1)*(4*x*k+2*x-1)*(4*x*k+4*x-1)/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jan 08 2013

G.f.: (1 - G(0))/x where G(k) = 1 - x/(1 - 2*x*(k + 1)/G(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Jan 30 2013

G.f.: 1/x + 1 - (2*x+1)/(G(0) + 2*x+1), where G(k)= 2*x*k - x - 1 - 2*(k+1)*x^2/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Jul 21 2013

G.f.: 1/x - Q(0)/x, where Q(k) = 1 - x*(2*k+1) - (2*k+2)*x^2/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 09 2013

Crossrefs

Sequence in context: A263687 A180891 A224529 * A177381 A289312 A127116

Adjacent sequences: A171148 A171149 A171150 * A171152 A171153 A171154

Keyword

easy,nonn

Author

Paul Barry, Dec 04 2009

Status

approved