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

1,2

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

Mathematica

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

Crossrefs

Cf. A047874. - Wouter Meeussen, Sep 30 2010

Sequence in context: A022519 A138439 A193563 * A305770 A145921 A304655

Adjacent sequences: A026842 A026843 A026844 * A026846 A026847 A026848

Keyword

nonn

Author

Bruce E. Sagan, Apr 06 2002

Extensions

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

Status

approved