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%I #6 May 06 2022 15:12:32
%S 1,1,5,73,4301,1065361,1079026325,4404504773593,72088402948928861,
%T 4722943066827454121761,1237982543178169058402322725,
%U 1298086594246614900499652230482793,5444532149619463867564918804810528611821,91343917667481554378430257939829428893551284401
%N G.f. A(x) satisfies: A(x) = 1 + x * A(4*x/(1 + 3*x)) / (1 - x).
%F G.f.: Sum_{k>=0} 2^(k*(k-1)) * (x/(1 - x))^k.
%F a(n) = Sum_{k=0..n} binomial(n-1,k-1) * 2^(k*(k-1)).
%t nmax = 13; A[_] = 0; Do[A[x_] = 1 + x A[4 x/(1 + 3 x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t Table[Sum[Binomial[n - 1, k - 1] 2^(k (k - 1)), {k, 0, n}], {n, 0, 13}]
%Y Cf. A006898, A053763, A135756 (partial sums), A353041.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Apr 19 2022
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