A014940 a(1)=1, a(n) = n*22^(n-1) + a(n-1).

1, 45, 1497, 44089, 1215369, 32137161, 825796489, 20780659593, 514663521417, 12587355699337, 304746506405001, 7316566123340937, 174431600326980745, 4133772410690139273, 97461091512107447433, 2287542179758700278921, 53480687617522807714953, 1245979840167792604460169

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (45,-528,484).

Programs

Mathematica

Table[(1+22^n (21n-1))/441,{n,20}] (* or *) CoefficientList[ Series[1/((1-x) (-1+22 x)^2),{x,0,20}],x] (* Harvey P. Dale, Apr 21 2011 *)

Formula

G.f.: x/((1-x)*(-1+22*x)^2). - Harvey P. Dale, Apr 21 2011

From Elmo R. Oliveira, May 18 2025: (Start)

E.g.f.: exp(x)*(1 + exp(21*x)*(462*x - 1))/441.

a(n) = (22^n*(21*n - 1) + 1)/441.

a(n) = 44*a(n-1) - 484*a(n-2) + 1 for n > 2.

a(n) = 45*a(n-1) - 528*a(n-2) + 484*a(n-3) for n > 3. (End)