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G.f.: A(x) = Sum_{n>=0} x^n / (1 - x^n - x^(2*n))^n.
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%I #12 Nov 08 2014 04:13:02

%S 1,1,2,3,6,6,17,14,36,44,81,90,225,234,456,682,1166,1598,2967,4182,

%T 7366,11215,18467,28658,48561,75216,123692,197415,322530,514230,

%U 841648,1346270,2191664,3528178,5723189,9229251,14975856,24157818,39147344,63258564,102444992,165580142

%N G.f.: A(x) = Sum_{n>=0} x^n / (1 - x^n - x^(2*n))^n.

%H Paul D. Hanna, <a href="/A223547/b223547.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ 1/sqrt(5) * ((1+sqrt(5))/2)^n. - _Vaclav Kotesovec_, Nov 08 2014

%e G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 6*x^5 + 17*x^6 + 14*x^7 +...

%e where

%e A(x) = 1 + x/(1-x-x^2) + x^2/(1-x^2-x^4)^2 + x^3/(1-x^3-x^6)^3 + x^4/(1-x^4-x^8)^4 + x^5/(1-x^5-x^10)^5 +...

%o (PARI) {a(n)=polcoeff(sum(m=0, n, x^m/(1-x^m-x^(2*m)+x*O(x^n))^m), n)}

%o for(n=0,45,print1(a(n),", "))

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 19 2013