login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A092119 EULER transform of A001511. 5
1, 1, 3, 4, 10, 13, 26, 35, 66, 88, 150, 202, 331, 442, 688, 919, 1394, 1848, 2716, 3590, 5174, 6796, 9589, 12542, 17440, 22680, 31055, 40208, 54420, 70096, 93772, 120256, 159380, 203436, 267142, 339573, 442478, 560050, 724302, 913198, 1173375, 1473622 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

From Gary W. Adamson, Feb 11 2010: (Start)

Given A000041, P(x) = A(x)/A(x^2) with P(x) = (1+x+2x^2+3x^3+5x^4+7x^5 + ...)

A(x) = (1+x+3x^2+4x^3+10x^4+13x^5 + ...),

A(x^2) = (1+x^2+3x^4+4x^6+10x^8+ ...), where A092119 = (1, 1, 3, 4, 10,...) =

Euler transform of the ruler sequence, A001511. (End)

Let M = triangle A173238 as an infinite lower triangular matrix. Then A092119 = Lim_{n->inf} M^n. Let P(x) = polcoeff A000041 = (1 + x + 2x^2 + 3x^3 + ...), and A(x) = polcoeff A092119. Then P(x) = A(x) / A(x^2), an example of a conjectured infinite set of operations (Cf. A173238). - Gary W. Adamson, Feb 13 2010

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

FORMULA

G.f.: 1/prod(k>=0, P(x^(2^k)) where P(x)=prod(k>=1, 1-x^k ). - Joerg Arndt, Jun 21 2011

PROG

(PARI)  N=66; x='x+O('x^N); /* that many terms */

gf=1/prod(e=0, ceil(log(N)/log(2)), eta(x^(2^e)));

Vec(gf) /* show terms */ /* Joerg Arndt, Jun 21 2011 */

CROSSREFS

Cf. A000041. - Gary W. Adamson, Feb 11 2010

Cf. A000041, A092119. - Gary W. Adamson, Feb 13 2010

Sequence in context: A031367 A073443 A257494 * A143372 A035594 A167273

Adjacent sequences:  A092116 A092117 A092118 * A092120 A092121 A092122

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Mar 29 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified April 23 06:26 EDT 2017. Contains 285314 sequences.