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 A186240 G.f. A(x) defined by A(x) = 1 +x*A(x) +x^2*A(x)^2 +3*x^3*A(x)^3. 0

%I

%S 1,1,2,7,21,66,228,799,2843,10357,38278,143012,539980,2056848,7892496,

%T 30483351,118416903,462348219,1813410078,7141608015,28229040165,

%U 111956307486,445374729396,1776704142348,7105896093588,28487216564476,114454156300136,460781265916312

%N G.f. A(x) defined by A(x) = 1 +x*A(x) +x^2*A(x)^2 +3*x^3*A(x)^3.

%H Vladimir Kruchinin, D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.

%F a(n) = 1/n*sum(j=0..n, binomial(n,j)*sum(i=j..n+j-1, binomial(j,i-j)*binomial(n-j,3*j-n-i-1)*3^(3*j-n-i-1))), n>0

%F Conjecture: 6*(2*n+3)*(n+1)*a(n) +(277*n^2-191*n-162)*a(n-1) +6*(-155*n^2+305*n-126)*a(n-2) -4*(181*n-195)*(n-2)*a(n-3) -5304*(n-2)*(n-3)*a(n-4)=0. - _R. J. Mathar_, Sep 27 2013

%t m = maxExponent = 20;

%t A[_] = 0; Do[A[x_] = 1 + x A[x] + x^2 A[x]^2 + 3 x^3 A[x]^3 + O[x]^m, {m}];

%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Aug 08 2018 *)

%K nonn

%O 0,3

%A _Vladimir Kruchinin_, Feb 15 2011

%E Typo in definition corrected by _R. J. Mathar_, Sep 27 2013

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Last modified May 27 12:58 EDT 2022. Contains 354097 sequences. (Running on oeis4.)