%I #8 Jan 06 2025 00:35:15
%S 1,2,346,5280932,6332299624282,548057409594239814752,
%T 3282684865686445066146128050420,
%U 1329153351023643434414727317328867397924832,35862023917618878200052422822926970148356592776600354650,63875599229358329592315180101212796802405282289343043273094466311541144
%N a(n) = A000172(n^2), where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.
%F Forms the logarithmic derivative of A216355 after ignoring initial term a(0).
%e L.g.f.: L(x) = 2*x + 346*x^2/2 + 5280932*x^3/3 + 6332299624282*x^4/4 + 548057409594239814752*x^5/5 +...
%e where exp(L(x)) = 1 + 2*x + 175*x^2 + 1760658*x^3 + 1583078442003*x^4 + 109611485085305859618*x^5 +...+ A216355(n)*x^n +...
%o (PARI) {a(n)=sum(k=0, n^2, binomial(n^2, k)^3)}
%o for(n=0, 15, print1(a(n), ", "))
%Y Cf. A216355, A166990, A216352, A216353, A216354, A000172.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Sep 04 2012