A016247 Expansion of 1/((1-x) * (1-6*x) * (1-11*x)).

1, 18, 241, 2910, 33565, 378546, 4219993, 46755846, 516329845, 5691721530, 62681496241, 689931815118, 7591862105101, 83526155988930, 918881752875145, 10108263503608086, 111194283871577893, 1223157434578690506, 13454853652313597665, 148004121407137586910, 1628049722868641531581

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (18, -83, 66).

Crossrefs

Cf. A016209, A016223, A016234.

Programs

Mathematica

CoefficientList[Series[1/((1-x)(1-6x)(1-11x)),{x,0,30}],x] (* or *) LinearRecurrence[{18,-83,66},{1,18,241},30] (* Harvey P. Dale, Sep 23 2012 *)

PARI

a(n) = (11^(n+2) - 2*6^(n+2) + 1)/50; \\ Joerg Arndt, Aug 13 2013

Formula

a(0)=1, a(1)=18, a(n)=17*a(n-1)-66*a(n-2)+1. - Vincenzo Librandi, Feb 10 2011

a(0)=1, a(1)=18, a(2)=241, a(n)=18*a(n-1)-83*a(n-2)+66*a(n-3). - Harvey P. Dale, Sep 23 2012

a(n) = (11^(n+2) - 2*6^(n+2) + 1)/50. [Yahia Kahloune, Aug 13 2013]

From Seiichi Manyama, May 05 2025: (Start)

a(n) = Sum_{k=0..n} 5^k * binomial(n+2,k+2) * Stirling2(k+2,2).

a(n) = Sum_{k=0..n} (-5)^k * 11^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2). (End)