A028200 Expansion of 1/((1-6x)(1-7x)(1-8x)(1-9x)).

1, 30, 565, 8550, 113701, 1388310, 15958405, 175419750, 1863406501, 19269697590, 195034120645, 1939826329350, 19018419228901, 184245490086870, 1767124523521285, 16805853434269350, 158682246543588901, 1489103597614860150, 13900428943759584325

Offset

0,2

Links

Matthew House, Table of n, a(n) for n = 0..1040

Index entries for linear recurrences with constant coefficients, signature (30,-335,1650,-3024).

Formula

If we define f(m,j,x) = Sum(binomial(m,k)*stirling2(k,j)*x^(m-k),k=j..m) then a(n-3) = f(n,3,6), (n >= 3). [Milan Janjic, Apr 26 2009]

a(n) = 17*a(n-1) - 72*a(n-2) + 7^(n+1) - 6^(n+1), a(0)=1, a(1)=30. - Vincenzo Librandi, Mar 11 2011

a(n) = (9^(n+3) - 3*8^(n+3) + 3*7^(n+3) - 6^(n+3))/6. [Yahia Kahloune, Jun 12 2013]

a(n) = 30*a(n-1) - 335*a(n-2) + 1650*a(n-3) - 3024*a(n-4). - Matthew House, Feb 11 2017

Mathematica

CoefficientList[Series[ 1/((1-6x)(1-7x)(1-8x)(1-9x)), {x, 0, 20} ], x]
LinearRecurrence[{30, -335, 1650, -3024}, {1, 30, 565, 8550}, 20] (* Harvey P. Dale, Mar 27 2023 *)

Prog

(PARI) Vec(1/((1-6*x)*(1-7*x)*(1-8*x)*(1-9*x)) + O(x^30)) \\ Michel Marcus, Feb 12 2017

Crossrefs

Sequence in context: A293103 A075510 A285168 * A028181 A177097 A028174

Adjacent sequences: A028197 A028198 A028199 * A028201 A028202 A028203

Keyword

nonn

Author

N. J. A. Sloane

Status

approved