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A171151
Expansion of (A(x)-1)/(x*A(x)), A(x) the g.f. of A004211.
1
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.
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Dec 04 2009
STATUS
approved