A090411 Expansion of g.f. (1-x)/(1-16*x).

1, 15, 240, 3840, 61440, 983040, 15728640, 251658240, 4026531840, 64424509440, 1030792151040, 16492674416640, 263882790666240, 4222124650659840, 67553994410557440, 1080863910568919040, 17293822569102704640, 276701161105643274240, 4427218577690292387840

Offset: 0

Author

Paul Barry, Nov 30 2003

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (16).

Crossrefs

Cf. A001025, A070775, A090407, A090408, A090409.

Programs

Mathematica

Join[{1, a = 15}, Table[a=16*a, {n,0,30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)
Join[{1},NestList[16#&,15,20]] (* Harvey P. Dale, Dec 28 2016 *)

PARI

a(n)=if(n,15<<(4*n-4),1) \\ Charles R Greathouse IV, Jun 10 2011

Formula

a(n) = 15*16^(n-1) + 0^n/16.

a(n) = Sum_{j=0..3, Sum_{k=0..n, C(4*n+j, 4*k)}}.

a(n) = (A070775(n) + A090407(n) + A001025(n) + A090408(n))/4.

From Elmo R. Oliveira, Mar 25 2025: (Start)

E.g.f.: (15*exp(16*x) + 1)/16.

a(n) = 16*a(n-1) for n > 1. (End)