A272108 Numerators of coefficients of the series of sqrt(-log(1-q)/q).

1, 1, 13, 35, 6271, 2211, 2760011, 1875133, 557576779, 13761972821, 3244313727791, 185892006151, 77616670784995799, 3796517116479937, 1261429981603803133, 4682424392750614127, 71254131149637283370867, 385105979676360971447, 2401927688678818378270288001

Offset

0,3

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.

Example

Coefficients begin: 1, 1/4, 13/96, 35/384, 6271/92160, ...

Maple

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

Mathematica

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

Prog

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

Crossrefs

Cf. A272109 (denominators).

Sequence in context: A221592 A135172 A183309 * A034119 A054285 A101103

Adjacent sequences: A272105 A272106 A272107 * A272109 A272110 A272111

Keyword

nonn,frac

Author

Jean-François Alcover, Apr 20 2016

Extensions

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

Edited by M. F. Hasler, Mar 16 2018

Status

approved