%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, <a href="http://com2mac.postech.ac.kr/resorce/
               Lecture_text.htm">Enumeration of graph coverings and surface branched 
               coverings</a>, 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