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%I #6 Mar 19 2016 09:03:56
%S 1,3,24,288,4440,82080,1752000,42178800,1127335680,33073099200,
%T 1055891810880,36435757294080,1351364788224000,53617083034314240,
%U 2266453101278568960,101705245560225146880,4829501671573344393600
%N Row 2 of table A128570.
%H Vaclav Kotesovec, <a href="/A128572/b128572.txt">Table of n, a(n) for n = 0..370</a>
%F G.f.: A(x) = 1 + 3x*R(x,3)^2, where R(x,3) = 1 + 4*x*R(x,4)^2, R(x,4) = 1 + 5*x*R(x,5)^2, ..., R(x,n) = 1 + (n+1)*x*R(x,n+1)^2, ... and R(x,n) is the g.f. of row n of table A128570.
%F a(n) ~ 8*n^2*A128318(n)/9. - _Vaclav Kotesovec_, Mar 19 2016
%o (PARI) {a(n)=local(A=1+(n+3)*x);for(j=0,n,A=1+(n+3-j)*x*A^2 +x*O(x^n)); polcoeff(A,n)}
%Y Cf. A128570 (triangle), other rows: A128318, A128571, A128573, A128574, A128575, A128576; A128577 (square of row 0), A128578 (main diagonal), A128579 (antidiagonal sums).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Mar 11 2007
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