A179488 G.f.: A(x) satisfies A(x) = x/(1 - (1-2x)*A( x/(1-2x) )).
1, 1, 2, 7, 32, 172, 1052, 7177, 53792, 437992, 3841772, 36060262, 360234512, 3812425912, 42576007352, 500022862357, 6157034292032, 79278216024592, 1064888929532492, 14890014669234922, 216315676347260912
Offset: 1
Keywords
Examples
G.f.: A(x) = x + x^2 + 2*x^3 + 7*x^4 + 32*x^5 + 172*x^6 + ... A(x) = x + x*A(x) + x*A(x)*A(x/(1-2x)) + x*A(x)*A(x/(1-2x))*A(x/(1-4x)) + x*A(x)*A(x/(1-2x))*A(x/(1-4x))*A(x/(1-6x)) + ...
Programs
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PARI
{a(n)=local(A=x+x^2);for(i=1,n,A=x/(1-(1-2*x)*subst(A,x,x/(1-2*x+x^2*O(x^n)))));polcoeff(A,n)}
Formula
G.f.: x/(1 - (1-2*x)*x/(1-2*x - (1-4*x)*x/(1-4*x - (1-6*x)*x/(1-6*x - (1-8*x)*x/(1-8*x - ... (continued fraction).
From Gary W. Adamson, Jul 21 2011: (Start)
a(n) = upper left term of M^(n-1), M = an infinite square production matrix as follows (with the odd integers as the main diagonal):
1, 1, 0, 0, 0, ...
1, 3, 1, 0, 0, ...
1, 1, 5, 1, 0, ...
1, 1, 1, 7, 1, ...
1, 1, 1, 1, 9, ...
... (End)
G.f.: 2/E(0) where E(k) = 1 + 1/(1 + 2*x/(1 - 2*(2*k+3)*x/E(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Sep 20 2012
G.f.: 1/Q(0) where Q(k) = 1 - x*(2*k+1)/( 1 - x/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 22 2013
G.f.: 1/x - Q(0)/x, where Q(k) = 1 - x/(1 - (2*k+1)*x/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Sep 27 2013