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A085351 Expansion of (1-3*x)/((1-4*x)*(1-5*x)). 4
1, 6, 34, 186, 994, 5226, 27154, 139866, 715714, 3644106, 18482674, 93461946, 471504034, 2374297386, 11938595794, 59961414426, 300880813954, 1508699037066, 7560675054514, 37872094749306, 189635351653474 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

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

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 *)

PROG

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

CROSSREFS

Cf. A027649, A085350, A085352.

Sequence in context: A084775 A327740 A229009 * A125343 A163350 A320746

Adjacent sequences: A085348 A085349 A085350 * A085352 A085353 A085354

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jun 24 2003

STATUS

approved

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Last modified November 30 10:04 EST 2022. Contains 358438 sequences. (Running on oeis4.)