A196661 Expansion of g.f. (1-2*x)/(1-7*x).

1, 5, 35, 245, 1715, 12005, 84035, 588245, 4117715, 28824005, 201768035, 1412376245, 9886633715, 69206436005, 484445052035, 3391115364245, 23737807549715, 166164652848005, 1163152569936035, 8142067989552245, 56994475926865715, 398961331488060005

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7).

Formula

a(0) = 1, a(n) = 5*7^(n-1) for n>0.

a(n) = Sum_{k=0..n} A193722(n,k)*2^k.

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

E.g.f.: (5*exp(7*x) + 2)/7.

a(n) = 7*a(n-1). (End)

Mathematica

Join[{1}, 5*7^Range[0, 25]] (* Paolo Xausa, May 25 2026 *)

Prog

(PARI) a(n)=if(n, 5*7^(n-1), 1) \\ Charles R Greathouse IV, Nov 21 2011

Crossrefs

Cf. A002001, A193577 (which is the same except for the initial 1), A193722.

Sequence in context: A290903 A155127 A239846 * A193577 A104532 A292839

Adjacent sequences: A196658 A196659 A196660 * A196662 A196663 A196664

Keyword

nonn,easy

Author

Philippe Deléham, Oct 05 2011

Status

approved