A168441 Expansion of 1/(1-x/(1-2x/(1-4x/(1-6x/(1-8x/(1-.... (continued fraction).

1, 1, 3, 17, 155, 2025, 34819, 743329, 18937707, 560071193, 18844479635, 710440531665, 29654234779771, 1357326276747721, 67589738142784803, 3637403230889380097, 210358430818676801675, 13009719599952748481145

Offset

0,3

Comments

Hankel transform is A168442.

Links

Table of n, a(n) for n=0..17.

Formula

G.f.: 1/(1-x-2x^2/(1-6x-24x^2/(1-14x-80x^2/(1-22x-168x^2/(1-30x-288x^2/(1-... (continued fraction).

a(n) = Sum_{k=0..n} A111106(n,k)*2^(n-k). - Philippe Deléham, Nov 28 2009

a(n) = upper left term of M^n, M = an infinite square production matrix as follows:

1, 1, 0, 0, 0, 0, ...

2, 2, 2, 0, 0, 0, ...

4, 4, 4, 4, 0, 0, ...

6, 6, 6, 6, 6, 0, ...

8, 8, 8, 8, 8, 8, ...

...

(where the series (1,2,4,6,8,...) = A004277, positive even integers prefaced with a 1). - Gary W. Adamson, Jul 19 2011

G.f. 1 + x/(G(0)-x) where G(k) = 1 - x*(2*k+2)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 28 2012

a(n) ~ 2^(2*n - 3/2) * n^(n-1) / exp(n). - Vaclav Kotesovec, Jan 23 2024

Mathematica

nmax = 20; CoefficientList[1 + x*Series[1/(1 - x + ContinuedFractionK[-2*k*x, 1, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jan 23 2024 *)

Crossrefs

Cf. A004277, A111106, A168442.

Sequence in context: A377810 A135751 A368444 * A001469 A110501 A274539

Adjacent sequences: A168438 A168439 A168440 * A168442 A168443 A168444

Keyword

easy,nonn

Author

Paul Barry, Nov 25 2009

Status

approved