%I #17 Nov 24 2016 09:33:13
%S 7,1225,1816871,7723802625,8591613499103635,23107999588635836875,
%T 446563431744711553183786875,17418085137491657842253233328125,
%U 1311214792748795041469921338623972253125,169160593483166517029276275055903719700625000,9261817633933021190882924368962406588490587588265625
%N a(n) is the numerator of intersection number <tau_2^(3n-3)>, n>=2.
%C For 'intersection numbers' see Section 1 in Itzykson and Zuber paper.
%H Gheorghe Coserea, <a href="/A278178/b278178.txt">Table of n, a(n) for n = 2..101</a>
%H Stavros Garoufalidis, Marcos Marino, <a href="https://arxiv.org/abs/0812.1195v4">Universality and asymptotics of graph counting problems in nonorientable surfaces</a>, arXiv:0812.1195 [math.CO], 2008.
%H C. Itzykson, J.-B. Zuber, <a href="https://arxiv.org/abs/hep-th/9201001">Combinatorics of the Modular Group II: the Kontsevich integrals</a>, arXiv:hep-th/9201001, 1991.
%F a(n) = numerator((3*n-3)!*4^n/((5*n-5)*(5*n-3)) * A269418(n)/A269419(n)) for n >= 2.
%e 7/240, 1225/144, 1816871/48, 7723802625/8, 8591613499103635/96, ...
%o (PARI)
%o A269418_seq(N) = {
%o my(y = vector(N)); y[1] = 1/48;
%o for (n = 2, N,
%o y[n] = (25*(n-1)^2-1)/48 * y[n-1] + 1/2*sum(k = 1, n-1, y[k]*y[n-k]));
%o concat(-1, y);
%o };
%o seq(N) = {
%o my(y = A269418_seq(N+2));
%o vector(N, g, (3*g)! * 4^(g+1) / ((5*g)*(5*g+2)) * y[g+2]);
%o };
%o apply(numerator, seq(12))
%Y Cf. A269418, A269419, A278179 (denominator).
%K nonn,frac
%O 2,1
%A _Gheorghe Coserea_, Nov 13 2016
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