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A203507 G.f.: Product_{n>=0} 1/(1-a(n)*x^(n+1))^3 = Sum_{n>=0} a(n)*x^n. 0

%I #7 Mar 30 2012 18:37:33

%S 1,3,15,82,504,3198,21592,147570,1045221,7464052,54549804,400487997,

%T 2990765270,22396990002,169881957174,1291189065086,9910770901971,

%U 76178174174205,590312326353680,4578346159792815,35745960436892046,279290158338688617

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

%e G.f.: A(x) = 1 + 3*x + 15*x^2 + 82*x^3 + 504*x^4 + 3198*x^5 + 21592*x^6 +...

%e where

%e A(x) = 1/((1-x)*(1-3*x^2)*(1-15*x^3)*(1-82*x^4)*(1-504*x^5)*...)^3.

%e Related expansion:

%e A(x)^(1/3) = 1 + x + 4*x^2 + 19*x^3 + 110*x^4 + 659*x^5 + 4355*x^6 +...

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

%Y Cf. A093637, A093638.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 02 2012

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