%I #5 Mar 30 2012 18:37:33
%S 1,1,21,3581,4638641,48800828001,4323567045653269,
%T 3282556699972913697517,21588080014422603968890377825,
%U 1239061910207197852963732743864398913,624049391401084282980615178692488088532058133
%N G.f.: [ Sum_{n>=0} (n+1)*(n+2)*(n+3)/3! * 3^(n*(n-1)) * x^n ]^(1/4).
%C Compare g.f. to: [Sum_{n>=0} (n+1)*(n+2)*(n+3)/3! * x^n ]^(1/4) = 1/(1-x).
%F a(n) == 1 (mod 4).
%e G.f.: A(x) = 1 + x + 21*x^2 + 3581*x^3 + 4638641*x^4 + 48800828001*x^5 +...
%e where
%e A(x)^4 = 1 + 4*x + 10*3^2*x^2 + 20*3^6*x^3 + 35*3^12*x^4 + 56*3^20*x^5 +...
%e more explicitly,
%e A(x)^4 = 1 + 4*x + 90*x^2 + 14580*x^3 + 18600435*x^4 + 195259926456*x^5 +...
%o (PARI) {a(n)=polcoeff(sum(m=0, n, (m+1)*(m+2)*(m+3)/3!*3^(m*(m-1))*x^m+x*O(x^n))^(1/4), n)}
%Y Cf. A202943.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Dec 26 2011