A272109 Denominators of coefficients of the series of sqrt(-log(1-q)/q).

1, 4, 96, 384, 92160, 40960, 61931520, 49545216, 16986931200, 475634073600, 125567395430400, 7972533043200, 3656522554933248000, 195014536263106560, 70205233054718361600, 280820932218873446400, 4582997613812014645248000, 26453088680011628544000

Offset

0,2

Comments

The function sqrt(-log(1-q)/q) is associated with the generating function of connected graphs enumeration

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

P. Flajolet, B. Salvy, and G. Schaeffer, Airy Phenomena and Analytic Combinatorics of Connected Graphs, Electronic Journal of Combinatorics, Volume 11(1), 2004, Research Paper #R34 page 8.

Maple

gf := sqrt(-log(1-q)/q) ;
taylor(%, q=0, 18) ;
gfun[seriestolist](%) ;
map(denom, %) ; # R. J. Mathar, Mar 15 2018

Mathematica

s = Sqrt[Log[1/(1 - q)]/q] + O[q]^20; CoefficientList[s, q] // Denominator

Prog

(PARI) Vec(apply(denominator, sqrt(-log(1-'q)/'q))) \\ M. F. Hasler, Mar 16 2018

Crossrefs

Cf. A272108 (numerators).

Sequence in context: A302121 A188895 A068114 * A203316 A359653 A202682

Adjacent sequences: A272106 A272107 A272108 * A272110 A272111 A272112

Keyword

nonn,frac

Author

Jean-François Alcover, Apr 20 2016

Extensions

Definition corrected by Juan Arias-de-Reyna, Mar 15 2018

Status

approved