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A280776 Numerators of coefficients in asymptotic expansion of C_n (number of connected chord diagrams, A000699).

%I A280776 #19 Jan 22 2017 21:24:04
%S A280776 1,-5,-43,-579,-44477,-5326191,-180306541,-203331297947,
%T A280776 -58726239094693,-781618285277957,-1025587838964854273,
%U A280776 -35763822710356866613,-330773478104531041960421,-237504847171108896327033959,-196526060612842999084524774697,-20633624138373135772483762873819
%N A280776 Numerators of coefficients in asymptotic expansion of C_n (number of connected chord diagrams, A000699).
%H A280776 Gheorghe Coserea, <a href="/A280776/b280776.txt">Table of n, a(n) for n = 0..101</a>
%H A280776 Michael Borinsky, <a href="https://arxiv.org/abs/1603.01236">Generating asymptotics for factorially divergent sequences</a>, arXiv preprint arXiv:1603.01236 [math.CO], 2016.
%e A280776 Coefficients are 1, -5/2, -43/8, -579/16, -44477/128, -5326191/1280, -180306541/3072, ...
%o A280776 (PARI)
%o A280776 A000699_seq(N) = {
%o A280776   my(a = vector(N)); a[1] = 1;
%o A280776   for (n=2, N, a[n] = sum(k=1, n-1, (2*k-1)*a[k]*a[n-k])); a;
%o A280776 };
%o A280776 seq(N) = my(C = 'x*Ser(A000699_seq(N))); Vec(x*exp(1-(2*C+C^2)/(2*x))/C);
%o A280776 apply(numerator, seq(16))  \\ _Gheorghe Coserea_, Jan 22 2017
%Y A280776 Cf. A000699, A280775, A111111, A280777, A280778, A280779, A280780, A280781.
%K A280776 sign,frac
%O A280776 0,2
%A A280776 _N. J. A. Sloane_, Jan 19 2017
%E A280776 More terms from _Gheorghe Coserea_, Jan 22 2017