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A287039 Row sums of A286782.

%I A287039 #16 Oct 25 2018 08:43:30
%S A287039 1,1,9,100,1323,20088,342430,6461208,133618275,3006094768,73139285178,
%T A287039 1914937983000,53720914023150,1608612191370000,51235727245542684,
%U A287039 1730349877484075120,61783682196714238755,2326122843950925857376,92117389831885545623650,3828375469597215729851928
%N A287039 Row sums of A286782.
%H A287039 Gheorghe Coserea, <a href="/A287039/b287039.txt">Table of n, a(n) for n = 0..302</a>
%H A287039 Michael Borinsky, <a href="https://arxiv.org/abs/1703.00840">Renormalized asymptotic enumeration of Feynman diagrams</a>, arXiv:1703.00840 [hep-th], 2017.
%H A287039 Luca G. Molinari, <a href="https://arxiv.org/abs/cond-mat/0401500">Hedin's equations and enumeration of Feynman's diagrams</a>, arXiv:cond-mat/0401500 [cond-mat.str-el], 2005.
%H A287039 Luca G. Molinari, Nicola Manini, <a href="https://arxiv.org/abs/cond-mat/0512342">Enumeration of many-body skeleton diagrams</a>, arXiv:cond-mat/0512342 [cond-mat.str-el], 2006.
%F A287039 a(n) ~ 4*exp(-1)/sqrt(Pi) * n^(3/2) * 2^n * n! * (1 - 19/(8*n) - 23/(128*n^2) + O(1/n^3)). (see Borinsky link) - _Gheorghe Coserea_, Oct 21 2017
%t A287039 max = 21; (* B(x) is A000699(x) *) B[_] = 0;
%t A287039 Do[B[x_] = x + x^2 D[B[x]^2/x, x] + O[x]^max // Normal, max];
%t A287039 Join[{1}, Drop[CoefficientList[(1-x/B[x])/x + O[x]^max, x], -2] Table[2n-1, {n, max-2}]] (* _Jean-François Alcover_, Oct 25 2018, from PARI *)
%o A287039 (PARI)
%o A287039 A000699_seq(N) = {
%o A287039   my(a = vector(N)); a[1] = 1;
%o A287039   for (n=2, N, a[n] = sum(k=1, n-1, (2*k-1)*a[k]*a[n-k])); a;
%o A287039 };
%o A287039 A286794_seq(N) = Vec((1-1/Ser(A000699_seq(N+1)))/x);
%o A287039 A287039_seq(N) = {
%o A287039   my(s = A286794_seq(N));
%o A287039   concat(1, vector(#s, n, (2*n-1)*s[n]));
%o A287039 };
%o A287039 A287039_seq(19)
%Y A287039 Cf. A000699, A049464, A286782, A287029.
%K A287039 nonn
%O A287039 0,3
%A A287039 _Gheorghe Coserea_, May 18 2017