%I #7 Oct 05 2024 20:17:12
%S 1,4,496,869824,21467623936,7881126729140224,44075357435370071351296,
%T 3802951448073847111253622882304,
%U 5104235473390420925196874786915866443776,107176786696765659714361271737312271270497663320064
%N G.f.: [ Sum_{n>=0} (n+1)*(n+2)/2 * 4^(n^2) * x^n ]^(1/3).
%F a(n) == 1 (mod 3).
%e G.f.: A(x) = 1 + 4*x + 496*x^2 + 869824*x^3 + 21467623936*x^4 +...
%e where
%e A(x)^3 = 1 + 3*4*x + 6*4^4*x^2 + 10*4^9*x^3 + 15*4^16*x^4 + 21*4^25*x^5 +...
%o (PARI) {a(n)=polcoeff(sum(m=0, n, (m+1)*(m+2)/2*4^(m^2)*x^m+x*O(x^n))^(1/3), n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A202942.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Mar 20 2012