A026845 Sum_{mu a partition of n} (f^mu/n!)^{-2} where f^mu is the number of standard Young tableaux of shape mu.

1, 8, 81, 1424, 32152, 1144937, 53178768, 3360267976, 268737034880, 26735641360265, 3222856389284352, 463078022054303432, 78131995260953112576, 15295767841794798044432, 3438384401028669096232665, 879589866427669147125523584, 254053056142392070125392290952

Offset: 1

Author

Bruce E. Sagan, Apr 06 2002

Keywords

• nonn

Comments

Arises from counting coverings of a genus g=2 Riemann surface - expansion of generating function A_g(q) = sum_{n>=0} a_{n,g} q^n where a_{n,g} = sum_{mu a partition of n} (f^mu/n!)^{2-2g}; note that A_0(q) = e^q and A_1(q) = prod_{i>=1} 1/(1-q^i).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..60

Crossrefs

Cf. A047874. - Wouter Meeussen, Sep 30 2010

Programs

Mathematica

(* version 4.0 *) Needs["DiscreteMath`Combinatorica`"]; Table[Tr[(n!/ (NumberOfTableaux /@ Partitions[n]))^2],{n,20}] (* Wouter Meeussen, Sep 30 2010 *)

Extensions

Terms 8 to 20 added by Wouter Meeussen, Sep 30 2010