A016157 Expansion of g.f. 1/((1-4*x)*(1-10*x)).

1, 14, 156, 1624, 16496, 165984, 1663936, 16655744, 166622976, 1666491904, 16665967616, 166663870464, 1666655481856, 16666621927424, 166666487709696, 1666665950838784, 16666663803355136, 166666655213420544

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..999
• Index entries for linear recurrences with constant coefficients, signature (14,-40).

Programs

Mathematica

Join[{a=1,b=14},Table[c=14*b-40*a;a=b;b=c,{n,60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
CoefficientList[Series[1/((1-4x)(1-10x)),{x,0,30}],x] (* or *) LinearRecurrence[{14,-40},{1,14},30] (* Harvey P. Dale, Jul 31 2025 *)

Formula

a(n) = ((7+sqrt(9))^(n+1) - (7-sqrt(9))^(n+1))/6. - Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009

From Vincenzo Librandi, Mar 18 2011: (Start)

a(n) = 14*a(n-1) - 40*a(n-2), n >= 2.

a(n) = 10*a(n-1) + 4^n = 4*a(n-1) + 10^n, n >= 1. (End)

a(n) = (5*10^n - 2*4^n)/3. - Bruno Berselli, Mar 19 2011

E.g.f.: exp(4*x)*(5*exp(6*x) - 2)/3. - Stefano Spezia, Sep 30 2023