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

Author

N. J. A. Sloane

Keywords

• nonn

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).

Crossrefs

Cf. A000453, A025211, A028025, A003468, A028165, A016109, A016075, A016094.

Programs

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 *)

PARI

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

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,3,6), (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