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A049291 Number of subgroups of index n in free group of rank 4. 1
1, 15, 625, 54335, 8563601, 2228419359, 893451975473, 523337983164799, 429463651385469649, 477364501208149290975, 699086688951391180496497, 1318072723102023442664430143, 3137514636520304660660007679505 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

M. Hall, Subgroups of finite index in free groups, Canad. J. Math., 1 (1949), 187-190.

P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 23.

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.

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(b).

LINKS

Table of n, a(n) for n=1..13.

FORMULA

a(n)=n*n!^3-Sum k!^3*a(n-k), k=1..n-1.

L.g.f.: Sum_{n>=1} a(n)*x^n/n = log( Sum_{n>=1} (n-1)!^3*x^n ). [From Paul D. Hanna, Apr 13 2009]

MATHEMATICA

ClearAll[a]; a[n_] := a[n] = n*n!^3 - Sum [k!^3*a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 13}]  (* Jean-Fran├žois Alcover, Oct 08 2012, from first formula *)

PROG

(PARI) {a(n)=n*polcoeff(log(sum(k=0, n, k!^3*x^k)+x*O(x^n)), n)} [From Paul D. Hanna, Apr 13 2009]

CROSSREFS

Cf. A003319, A027837, A049290-A049295.

Sequence in context: A012210 A203172 A081022 * A092958 A222268 A223203

Adjacent sequences:  A049288 A049289 A049290 * A049292 A049293 A049294

KEYWORD

easy,nice,nonn

AUTHOR

Valery A. Liskovets

EXTENSIONS

More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 17 2001

STATUS

approved

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Last modified October 20 20:53 EDT 2014. Contains 248371 sequences.