A085351 Expansion of (1-3*x)/((1-4*x)*(1-5*x)).

1, 6, 34, 186, 994, 5226, 27154, 139866, 715714, 3644106, 18482674, 93461946, 471504034, 2374297386, 11938595794, 59961414426, 300880813954, 1508699037066, 7560675054514, 37872094749306, 189635351653474

Offset: 0

Author

Paul Barry, Jun 24 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A085350. Second binomial transform of poly-Bernoulli numbers A027649.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-20).

Crossrefs

Cf. A027649, A085350, A085352.

Programs

Mathematica

CoefficientList[Series[(1-3x)/((1-4x)(1-5x)),{x,0,20}],x] (* or *) LinearRecurrence[{9,-20},{1,6},30] (* Harvey P. Dale, Jan 07 2022 *)

PARI

Vec((1 - 3*x) / ((1 - 4*x)*(1 - 5*x)) + O(x^25)) \\ Colin Barker, Jun 25 2020

Formula

G.f.: (1-3*x)/((1-4*x)*(1-5*x)).

a(n) = 2*5^n - 4^n.

a(n) = 9*a(n-1) - 20*a(n-2) for n>1. - Colin Barker, Jun 25 2020