A128625 Expansion of (1+3*x)/(1-5*x).

1, 8, 40, 200, 1000, 5000, 25000, 125000, 625000, 3125000, 15625000, 78125000, 390625000, 1953125000, 9765625000, 48828125000, 244140625000, 1220703125000, 6103515625000, 30517578125000, 152587890625000, 762939453125000, 3814697265625000, 19073486328125000

Offset: 0

Author

Paul Barry, Mar 14 2007

Keywords

• easy
• nonn

Comments

Binomial transform of A102900(n+1).

Hankel transform is := 1,-24,0,0,0,0,0,0,0,0,0,... - Philippe Deléham, Nov 02 2008

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5).

Crossrefs

Cf. A102900.

Programs

Magma

[n eq 0 select 1 else 8*5^(n-1): n in [0..50]]; // G. C. Greubel, Mar 12 2024

Mathematica

CoefficientList[Series[(1 + 3 x)/(1 - 5 x), {x, 0, 50}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 21 2011 *)
Join[{1},NestList[5#&,8,30]] (* or *) LinearRecurrence[{5},{1,8},30] (* Harvey P. Dale, Dec 23 2021 *)

SageMath

[(8*5^n - 3*int(n==0))//5 for n in range(51)] # G. C. Greubel, Mar 12 2024

Formula

a(n) = (8/5)*5^n - (3/5)*0^n.

a(0)=1, a(n) = Sum_{k=0..n} ((n+k)/n)*binomial(n,k)*2^(n-k)*3^k, n > 0.

E.g.f.: (8*exp(5*x) - 3)/5. - G. C. Greubel, Mar 12 2024