A026845 - OEIS

A026845

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

%I #17 Jun 27 2022 21:18:48

%S 1,8,81,1424,32152,1144937,53178768,3360267976,268737034880,

%T 26735641360265,3222856389284352,463078022054303432,

%U 78131995260953112576,15295767841794798044432,3438384401028669096232665,879589866427669147125523584,254053056142392070125392290952

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

%C 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).

%H Alois P. Heinz, <a href="/A026845/b026845.txt">Table of n, a(n) for n = 1..60</a>

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

%Y Cf. A047874. - _Wouter Meeussen_, Sep 30 2010

%K nonn

%O 1,2

%A _Bruce E. Sagan_, Apr 06 2002

%E Terms 8 to 20 added by _Wouter Meeussen_, Sep 30 2010