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A237650 G.f. satisfies: A(x) = (1+x+x^2)^3 * A(x^2)^2.

%I A237650 #7 Mar 13 2015 23:36:23
%S A237650 1,3,12,25,75,144,357,615,1380,2285,4767,7488,14817,22707,43068,63769,
%T A237650 116667,169584,301589,427815,741396,1037149,1761087,2418432,4025153,
%U A237650 5465955,8956716,11986009,19330347,25633296,40835973,53508711,84129156,109392269,170278047,219206976
%N A237650 G.f. satisfies: A(x) = (1+x+x^2)^3 * A(x^2)^2.
%F A237650 The odd-indexed bisection of A195586.
%F A237650 The 3rd self-convolution of A237651.
%F A237650 G.f. A(x) satisfies:
%F A237650 (1) A(x) = Product_{n>=0} ( 1 + x^(2^n) + x^(2*2^n) )^(3*2^n).
%F A237650 (2) A(x) / A(-x) = (1+x+x^2)^3 / (1-x+x^2)^3.
%e A237650 G.f.: A(x) = 1 + 3*x + 12*x^2 + 25*x^3 + 75*x^4 + 144*x^5 + 357*x^6 +...
%e A237650 where:
%e A237650 A(x) = (1+x+x^2)^3 * (1+x^2+x^4)^6 * (1+x^4+x^8)^12 * (1+x^8+x^16)^24 * (1+x^16+x^32)^48 *...* (1 + x^(2^n) + x^(2*2^n))^(3*2^n) *...
%o A237650 (PARI) {a(n)=local(A=1+x);for(i=1,#binary(n),A=(1+x+x^2)^3*subst(A^2,x,x^2) +x*O(x^n));polcoeff(A,n)}
%o A237650 for(n=0,50,print1(a(n),", "))
%o A237650 (PARI) {a(n)=local(A=1+x);A=prod(k=0,#binary(n),(1+x^(2^k)+x^(2*2^k)+x*O(x^n))^(3*2^k));polcoeff(A,n)}
%o A237650 for(n=0,50,print1(a(n),", "))
%Y A237650 Cf. A195586, A237651, A237647.
%K A237650 nonn
%O A237650 0,2
%A A237650 _Paul D. Hanna_, May 04 2014