A016296 Expansion of g.f. 1/((1 - 2*x)*(1 - 5*x)*(1 - 7*x)).

1, 14, 137, 1162, 9165, 69342, 511393, 3709874, 26619989, 189594790, 1343438889, 9485451066, 66805055773, 469669890158, 3297861746225, 23135894831938, 162205576930917, 1136710604184246, 7963332057891001, 55775113548767690, 390584740560075821, 2734887912516137854

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..1182
• Index entries for linear recurrences with constant coefficients, signature (14,-59,70).

Programs

Mathematica

CoefficientList[Series[1/((1 - 2 x) (1 - 5 x) (1 - 7 x)), {x, 0, 18}], x] (* Michael De Vlieger, Jan 31 2018 *)
LinearRecurrence[{14,-59,70},{1,14,137},30] (* Harvey P. Dale, Aug 11 2021 *)

Sage

[((7^n - 2^n)/5-(5^n - 2^n)/3)/2 for n in range(2,21)] # Zerinvary Lajos, Jun 05 2009

Formula

a(n-2) = ((7^n - 2^n)/5 - (5^n - 2^n)/3)/2. - Zerinvary Lajos, Jun 05 2009

From Vincenzo Librandi, Mar 16 2011: (Start)

a(n) = 14*a(n-1) - 59*a(n-2) + 70*a(n-3), n >= 3.

a(n) = 12*a(n-1) - 35*a(n-2) + 2^n, n >= 2. (End)

E.g.f.: exp(2*x)*(8 - 125*exp(3*x) + 147*exp(5*x))/30. - Stefano Spezia, Feb 08 2025