A278178 a(n) is the numerator of intersection number <tau_2^(3n-3)>, n>=2.

7, 1225, 1816871, 7723802625, 8591613499103635, 23107999588635836875, 446563431744711553183786875, 17418085137491657842253233328125, 1311214792748795041469921338623972253125, 169160593483166517029276275055903719700625000, 9261817633933021190882924368962406588490587588265625

Offset

2,1

Comments

For 'intersection numbers' see Section 1 in Itzykson and Zuber paper.

Links

Gheorghe Coserea, Table of n, a(n) for n = 2..101

Stavros Garoufalidis, Marcos Marino, Universality and asymptotics of graph counting problems in nonorientable surfaces, arXiv:0812.1195 [math.CO], 2008.

C. Itzykson, J.-B. Zuber, Combinatorics of the Modular Group II: the Kontsevich integrals, arXiv:hep-th/9201001, 1991.

Formula

a(n) = numerator((3*n-3)!*4^n/((5*n-5)*(5*n-3)) * A269418(n)/A269419(n)) for n >= 2.

Example

7/240, 1225/144, 1816871/48, 7723802625/8, 8591613499103635/96, ...

Prog

(PARI)
A269418_seq(N) = {
  my(y  = vector(N)); y[1] = 1/48;
  for (n = 2, N,
       y[n] = (25*(n-1)^2-1)/48 * y[n-1] + 1/2*sum(k = 1, n-1, y[k]*y[n-k]));
  concat(-1, y);
};
seq(N) = {
  my(y = A269418_seq(N+2));
  vector(N, g, (3*g)! * 4^(g+1) / ((5*g)*(5*g+2)) * y[g+2]);
};
apply(numerator, seq(12))

Crossrefs

Cf. A269418, A269419, A278179 (denominator).

Sequence in context: A202133 A229431 A159994 * A190266 A119181 A152518

Adjacent sequences: A278175 A278176 A278177 * A278179 A278180 A278181

Keyword

nonn,frac

Author

Gheorghe Coserea, Nov 13 2016

Status

approved