A249996 Expansion of 1/((1+2*x)*(1+3*x)*(1-4*x)).

1, -1, 15, -5, 191, 99, 2455, 3515, 33231, 74899, 474695, 1371435, 7071871, 23520899, 108399735, 390617755, 1691480111, 6378762099, 26676785575, 103221406475, 423343881951, 1661998662499, 6742129440215, 26686105001595, 107591675061391, 427824901526099, 1718925069371655

Offset: 0

Author

Alex Ratushnyak, Dec 28 2014

Keywords

• sign
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,14,24).

Crossrefs

Cf. A016269: expansion of 1/((1-2*x)*(1-3*x)*(1-4*x)).

Cf. A249992, A249993, A249994, A249995.

Programs

Magma

[(2^(2*n+3) +(-1)^n*(3^(n+3) -7*2^(n+1)))/21: n in [0..40]]; // G. C. Greubel, Oct 11 2022

Mathematica

LinearRecurrence[{-1,14,24}, {1,-1,15}, 41] (* G. C. Greubel, Oct 11 2022 *)

PARI

Vec(1/((1+2*x)*(1+3*x)*(1-4*x)) + O(x^50)) \\ Michel Marcus, Dec 29 2014

SageMath

[(2^(2*n+3) +(-1)^n*(3^(n+3) -7*2^(n+1)))/21 for n in range(41)] # G. C. Greubel, Oct 11 2022

Formula

G.f.: 1 / ((1+2*x)*(1+3*x)*(1-4*x)).

a(n) = ( 2^(3+2*n) + (3^(3+n)-7*2^(1+n))*(-1)^n )/21. - Colin Barker, Dec 29 2014

a(n) = -a(n-1) + 14*a(n-2) + 24*a(n-3). - Colin Barker, Dec 29 2014

E.g.f.: (1/21)*(27*exp(-3*x) - 14*exp(-2*x) + 8*exp(4*x)). - G. C. Greubel, Oct 11 2022