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A179277 A(x) = C(x) * C(x^2) * C(x^4) * C(x^8) *...; C = Catalan, A000108; A(x)/A(x^2) satisfies C(x) 2
1, 1, 3, 6, 19, 50, 158, 492, 1635, 5466, 18794, 65332, 230414, 820052, 2945436, 10654808, 38795523, 142045610, 522694866, 1931912036, 7169014298, 26698782108, 99756713732, 373839656616, 1404795235438, 5292114330180 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Let the sequence = A(x) = (1 + x + 3x^2 + 6x^3 + 19x^4 + ...).

Then A(x)/A(x^2) = C(x) = (1 + x + 2x^2 + 5x^3 + 14x^4 + ...).

LINKS

Table of n, a(n) for n=0..25.

FORMULA

Let M = an infinite lower triangular matrix with A000108 in each column but

shifted down twice from the previous column, for k>0. Lim_{n->inf.} M^n =

A179277, the left shifted vector considered as a sequence: (1 + x + 3x^2 + ...)

a(n) = sum_{l=0..n/2} a(l)*A000108(n-2*l). [From R. J. Mathar, Jul 09 2010]

EXAMPLE

The generating triangle = M:

1;

1;

2, 1;

5, 1;

14, 2, 1;

42, 5, 1;

132, 14, 2, 1;

429, 42, 5, 1;

1430, 132, 14, 2, 1;

4862, 429, 42, 5, 1;

16796, 1430, 132, 14, 2, 1;

...

Then take powers of this matrix, obtaining a left-shifted vector considered

as a sequence = A179277.

MAPLE

Contribution from R. J. Mathar, Jul 09 2010: (Start)

A000108 := proc(n) binomial(2*n, n)/(n+1) ; end proc:

A179277 := proc(n) if n <= 1 then 1; else add( procname(l)*A000108(n-2*l), l=0..n/2) ; end if; end proc:

seq(A179277(n), n=0..80) ; (End)

CROSSREFS

A000108

Sequence in context: A148567 A148568 A003162 * A129417 A132335 A148569

Adjacent sequences:  A179274 A179275 A179276 * A179278 A179279 A179280

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Jul 07 2010

EXTENSIONS

More terms from R. J. Mathar, Jul 09 2010

STATUS

approved

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Last modified July 23 08:51 EDT 2017. Contains 289686 sequences.