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A092119 EULER transform of A001511. 7
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->infinity} 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/Product_{k>=0} P(x^(2^k)) where P(x) = Product_{k>=1} (1 - x^k). - Joerg Arndt, Jun 21 2011

MATHEMATICA

m = 42;

1/Product[QPochhammer[x^(2^k)], {k, 0, Log[2, m]//Ceiling}] + O[x]^m // CoefficientList[#, x]& (* Jean-Fran├žois Alcover, Jan 14 2020, after Joerg Arndt *)

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: A073443 A257494 A302347 * A143372 A035594 A167273

Adjacent sequences:  A092116 A092117 A092118 * A092120 A092121 A092122

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Mar 29 2004

STATUS

approved

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Last modified October 20 18:32 EDT 2020. Contains 337905 sequences. (Running on oeis4.)