A021021 Expansion of 1/((1-10x)(1-11x)(1-12x)).

1, 33, 727, 13365, 221431, 3428733, 50631967, 721942485, 10021257511, 136192514733, 1819621847407, 23973890545605, 312209398691191, 4026262617877533, 51492399583946047, 653858524870924725

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (33,-362,1320)

Formula

If we define f(m,j,x) = Sum_{k=j..m} binomial(m,k)*Stirling2(k,j)*x^(m-k) then a(n-2) = f(n,2,10) for n >= 2. - Milan Janjic, Apr 26 2009

a(n) = 33*a(n-1) - 362*a(n-2) + 1320*a(n-3), n >= 3. - Vincenzo Librandi, Mar 18 2011

a(n) = 23*a(n-1) - 132*a(n-2) + 10^n, n >= 2. - Vincenzo Librandi, Mar 18 2011

a(n) = 6*12^(n+1) - 11^(n+2) + 5*10^(n+1). - R. J. Mathar, Mar 18 2011

Mathematica

CoefficientList[Series[1/((1-10x)(1-11x)(1-12x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{33, -362, 1320}, {1, 33, 727}, 30] (* Harvey P. Dale, Apr 27 2012 *)

Crossrefs

Sequence in context: A028020 A025130 A081141 * A164750 A100788 A051565

Adjacent sequences: A021018 A021019 A021020 * A021022 A021023 A021024

Keyword

nonn

Author

N. J. A. Sloane

Status

approved