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A193189 G.f.: A(x) = Sum_{n>=0} x^n / Product_{k=1..n} (1 - 3^(n-k)*x^k). 3

%I #6 Mar 30 2012 18:37:27

%S 1,1,2,5,21,143,1669,33857,1193884,73213398,7782525256,1435756825940,

%T 458580933408939,254032043880526955,243538638598143498007,

%U 404846375019050008264450,1164567481729705354758216971,5808325975811136555473345566847

%N G.f.: A(x) = Sum_{n>=0} x^n / Product_{k=1..n} (1 - 3^(n-k)*x^k).

%F G.f. satisfies: A(3*x) = Sum_{n>=0} 3^n*x^n / Product_{k=1..n} (1 - 3^n*x^k).

%e G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 21*x^4 + 143*x^5 + 1669*x^6 +...

%e where:

%e A(x) = 1 + x/(1-x) + x^2/((1-3*x)*(1-x^2)) + x^3/((1-9*x)*(1-3*x^2)*(1-x^3)) + x^4/((1-27*x)*(1-9*x^2)*(1-3*x^3)*(1-x^4)) + ...

%o (PARI) {a(n)=local(A=1);polcoeff(sum(m=0,n,x^m/prod(k=1,m,1-3^(m-k)*x^k +x*O(x^n))),n)}

%Y Cf. A193188, A193190, A193191.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 17 2011

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