This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A115868 #16 Aug 05 2024 11:26:24 %S A115868 1,1,1,1,2,2,4,6,11,18,39,70,153,321,721,1612,3792,8896,21498,52230, %T A115868 128994,320786,806582,2040912,5205311,13352470,34460430,89384609 %N A115868 Invariants for a hidden action of S_(n+1) on Cayley trees with n vertices. %C A115868 This is the multiplicity of the trivial module in a sequence of modules of dimension (n-1)^(n-3) over the symmetric groups S_n. The restriction of these modules to S_(n-1) is given by the action on trees. %F A115868 No simple formula known, only a complicated sum over partitions. %F A115868 It seems that a(n+1) = A000055(n) + A051573(n) - A000081(n). - _Andrey Zabolotskiy_, Aug 05 2024 %e A115868 M[6]=s[2, 1, 1, 1, 1] + 3 s[2, 2, 2] + 2 s[3, 1, 1, 1] + 2 s[3, 2, 1] + s[4, 1, 1] + 4 s[4, 2] + s[5, 1] + 2 s[6] as a sum of Schur functions hence a[6]=2. %Y A115868 Cf. A000055 and A000272. %Y A115868 Cf. A000081, A051573, A098091. %K A115868 nonn,more %O A115868 2,5 %A A115868 _F. Chapoton_, Mar 14 2006 %E A115868 Five more terms added by _F. Chapoton_, Mar 08 2020