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

1,3

Links

Table of n, a(n) for n=1..21.

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

Example

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)) + ...

Prog

(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)}

Crossrefs

Cf. variants: A074664, A179489.

Sequence in context: A125277 A321688 A222013 * A191809 A161392 A161393

Adjacent sequences: A179485 A179486 A179487 * A179489 A179490 A179491

Keyword

nonn

Author

Paul D. Hanna, Aug 13 2010

Status

approved