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A092119 EULER transform of A001511. 7

%I

%S 1,1,3,4,10,13,26,35,66,88,150,202,331,442,688,919,1394,1848,2716,

%T 3590,5174,6796,9589,12542,17440,22680,31055,40208,54420,70096,93772,

%U 120256,159380,203436,267142,339573,442478,560050,724302,913198,1173375,1473622

%N EULER transform of A001511.

%C From _Gary W. Adamson_, Feb 11 2010: (Start)

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

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

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

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

%C 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

%H Alois P. Heinz, <a href="/A092119/b092119.txt">Table of n, a(n) for n = 0..1000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F G.f.: 1/prod(k>=0, P(x^(2^k)) where P(x)=prod(k>=1, 1-x^k ). - _Joerg Arndt_, Jun 21 2011

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

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

%o Vec(gf) /* show terms */ /* _Joerg Arndt_, Jun 21 2011 */

%Y Cf. A000041. - _Gary W. Adamson_, Feb 11 2010

%Y Cf. A000041, A092119. - _Gary W. Adamson_, Feb 13 2010

%K nonn

%O 0,3

%A _Vladeta Jovovic_, Mar 29 2004

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Last modified November 17 23:26 EST 2019. Contains 329242 sequences. (Running on oeis4.)