A278179 - OEIS

%I #19 Nov 24 2016 09:33:05

%S 240,144,48,8,96,1,32,1,32,1,8,1,16,1,64,1,32,1,32,1,64,1,16,1,16,1,8,

%T 1,16,1,128,1,32,1,32,1,64,1,64,1,64,1,4,1,8,1,32,1,16,1,16,1,32,1,16,

%U 1,16,1,8,1,16,1,256,1,32,1,32,1,64,1,64,1,64,1,16,1,32,1,128,1,64,1,64,1,128

%N a(n) is the denominator 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="/A278179/b278179.txt">Table of n, a(n) for n = 2..1025</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) = denominator((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(denominator, seq(85))

%Y Cf. A269418, A269419, A278178 (numerator).

%K nonn,frac

%O 2,1

%A _Gheorghe Coserea_, Nov 13 2016