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A056198 Defined by Product 1/(1-x^k)^a_k, k=1..inf = 1+x+2*Sum(a_k*x^k, k=2..inf). 1


%S 1,2,3,9,24,76,236,785,2634,9106,31870,113371,407438,1479526,5415700,

%T 19970119,74096864,276466199,1036598162,3903844089,14760093096,

%U 56006631629,213206289068,814045174247,3116569685906,11961635892951

%N Defined by Product 1/(1-x^k)^a_k, k=1..inf = 1+x+2*Sum(a_k*x^k, k=2..inf).

%C Klein and Shadmi call these "Organic Numbers".

%H Gan Adam, <a href="http://www.omath.org.il/site/index.asp?depart_id=112431&amp;lat=en">One Mathematics</a>

%H Moshe Klein and Doron Shadmi, <a href="http://www.omath.org.il/image/users/112431/ftp/my_files/OM-Sweden_C.pps">Organic Mathematics</a>

%p a := [1,2]; for n from 3 to 30 do L := series( mul( (1-x^k)^(-a[k]),k=1..n-1)/(1-x^n)^b, x,n+1); t1 := coeff(L,x,n); R := series( 1+x+2*add(a[k]*x^k,k=2..n-1)+2*b*x^n, x, n+1); t2 := coeff(R,x,n); t3 := solve(t1-t2,b); a := [op(a),t3]; od: A056198 := n->a[n];

%Y Recurrence suggested by that for A000669.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Aug 05 2000

%E Antti Karttunen discovered that the Klein-Shadmi "Organic Numbers" are the same as this sequence. - _N. J. A. Sloane_, Apr 02 2011

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Last modified April 21 06:10 EDT 2021. Contains 343146 sequences. (Running on oeis4.)