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%I #10 Jun 30 2021 17:56:16
%S 1,2,5,14,43,142,496,1808,6807,26270,103357,412942,1670572,6828824,
%T 28159880,116997296,489271039,2057800158,8698624303,36936288650,
%U 157474552403,673830974654,2892864930292,12457038200008,53789813903620
%N Antidiagonal sums of table A088925, which lists coefficients T(n,k) of x^n*y^k in f(x,y) that satisfies f(x,y) = 1/(1-x-y) + xy*f(x,y)^3.
%H Michael De Vlieger, <a href="/A088927/b088927.txt">Table of n, a(n) for n = 0..300</a>
%H Paul Barry, <a href="https://arxiv.org/abs/2104.01644">Centered polygon numbers, heptagons and nonagons, and the Robbins numbers</a>, arXiv:2104.01644 [math.CO], 2021.
%F a(n) = sum(k=0, n, sum(i=0, k, C(n, 2i)*C(n-2i, k-i)*A001764(i) )), where A001764(i)=(3i)!/[i!(2i+1)! ] (from Michael Somos).
%F G.f. satisfies A(x) = 1/(1-2x) + x^2*A(x)^3.
%F a(n) ~ (2 + 3*sqrt(3)/2)^(n + 3/2) / (3^(7/4) * sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Oct 10 2020
%e A(x) = 1/(1-2x) + x^2*A(x)^3 since 1/(1-2x) = 1 + 2x + 4x^2 + 8x^3 +... and x^2*A(x)^3 = 1x^2 + 6x^3 + 27x^4 + 110x^5 +...
%t Table[Sum[Sum[Binomial[n, 2*i] * Binomial[n - 2*i, k - i] * (3*i)! / (i! * (2*i + 1)!), {i, 0, k}], {k, 0, n}], {n, 0, 25}] (* _Vaclav Kotesovec_, Oct 10 2020 *)
%Y Cf. A088925 (table), A088926 (diagonal), A001764.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 23 2003