A016094 Expansion of 1/((1-9*x)*(1-10*x)*(1-11*x)*(1-12*x)).

1, 42, 1105, 23310, 431221, 7309722, 116419465, 1769717670, 25948716541, 369730963602, 5147200519825, 70298695224030, 944897655707461, 12530341519244682, 164265473257148185, 2132247784185258390

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (42,-659,4578,-11880)

Formula

If we define f(m,j,x) = Sum_{k=j..m} binomial(m,k)*Stirling2(k,j)*x^(m-k) then a(n-3) = f(n,3,9), n >= 3. - Milan Janjic, Apr 26 2009

a(n) = 42*a(n-1) - 659*a(n-2) + 4578*a(n-3) - 11880*a(n-4), n >= 4. - Vincenzo Librandi, Mar 18 2011

a(n) = 23*a(n-1) - 132*a(n-2) + 10^(n+1) - 9^(n+1), n >= 2. - Vincenzo Librandi, Mar 18 2011

a(n) = 5*10^(n+2) + 2*12^(n+2) - 11^(n+3)/2 - 3*9^(n+2)/2. - R. J. Mathar, Mar 19 2011

Mathematica

CoefficientList[Series[1/((1-9x)(1-10x)(1-11x)(1-12x)) , {x, 0, 20}], x] (* or *) LinearRecurrence[{42, -659, 4578, -11880}, {1, 42, 1105, 23310}, 20] (* Harvey P. Dale, Dec 14 2021 *)

Crossrefs

Sequence in context: A163741 A140404 A075511 * A004361 A264178 A260584

Adjacent sequences: A016091 A016092 A016093 * A016095 A016096 A016097

Keyword

nonn

Author

N. J. A. Sloane

Status

approved