Search: id:A049290 Results 1-1 of 1 results found. %I A049290 %S A049290 1,1,1,1,3,1,1,7,13,1,1,15,97,71,1,1,31,625,2143,461,1,1,63,3841,54335, %T A049290 68641,3447,1,1,127,23233,1321471,8563601,3011263,29093,1,1,255,139777, %U A049290 31817471,1035045121,2228419359,173773153,273343,1,1,511,839425 %N A049290 Array T(n,k) = number of subgroups of index k in free group of rank n, read by antidiagonals. %D A049290 P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 23. %D A049290 V. A. Liskovets and A. Mednykh, Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces, Commun. in Algebra, 28, No. 4 (2000), 1717-1738. %D A049290 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(b). %H A049290 J. H. Kwak and J. Lee, Enumeration of graph coverings and surface branched coverings, Lecture Note Series 1 (2001), Com^2MaC-KOSEF, Korea. See chapter 3. %e A049290 Array T(n,k) (n >= 1, k >= 1) begins: %e A049290 1,1,1,1,1,1,1,... %e A049290 1,3,13,71,461,... %e A049290 1,7,97,2143,... %e A049290 1,15,625,54335,... %p A049290 T:= proc(n,k) option remember; k* k!^(n-1) -add (j!^(n-1) *T(n, k-j), j=1..k-1) end: seq (seq (T(d+1-k, k), k=1..d), d=1..10); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 29 2009] %Y A049290 Rows give A003319, A027837, A049291, columns give A049294, A049295. main diagonal is A057014. %Y A049290 Sequence in context: A075440 A137470 A112492 this_sequence A147990 A134567 A131932 %Y A049290 Adjacent sequences: A049287 A049288 A049289 this_sequence A049291 A049292 A049293 %K A049290 nonn,easy,nice,tabl %O A049290 1,5 %A A049290 N. J. A. Sloane (njas(AT)research.att.com), Sep 09 2000 %E A049290 More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 29 2009 Search completed in 0.001 seconds