OFFSET
0,2
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).
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
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 *)
PROG
(Magma) [n eq 0 select 1 else 8*5^(n-1): n in [0..50]]; // G. C. Greubel, Mar 12 2024
(SageMath) [(8*5^n - 3*int(n==0))//5 for n in range(51)] # G. C. Greubel, Mar 12 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 14 2007
STATUS
approved