A103878 Expansion of x / ((1-12x)(1-15x)(1-20x)(1-30x)(1-60x)).

0, 1, 137, 12019, 874853, 58067611, 3673451957, 226576032859, 13790081534933, 833490615528571, 50196582942983477, 3017503478665411099, 181223386494229073813, 10878637590184410995131, 652876078076017863582197, 39177315318319288337595739

Offset: 0

Author

Ralf Stephan, Feb 20 2005

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..562
• Jerry Metzger and Thomas Richards, A Prisoner Problem Variation, Journal of Integer Sequences, Vol. 18 (2015), Article 15.2.7.
• Index entries for linear recurrences with constant coefficients, signature (137,-6750,153000,-1620000,6480000).

Crossrefs

Cf. A001242.

Programs

Mathematica

CoefficientList[Series[x/((1-12x)(1-15x)(1-20x)(1-30x)(1-60x)),{x,0,20}],x] (* or *) LinearRecurrence[ {137,-6750,153000,-1620000,6480000},{0,1,137,12019,874853},20] (* Harvey P. Dale, Aug 31 2024 *)

PARI

concat(0, Vec(x/(-6480000*x^5+1620000*x^4-153000*x^3+6750*x^2-137*x+1) + O(x^100))) \\ Colin Barker, Apr 26 2015

Formula

a(n) = (1/12) (12^n - 4*15^n + 6*20^n - 4*30^n + 60^n).